Vehicle motion control device and method

ABSTRACT

The objective of the present invention is to provide a vehicle motion control device capable of controlling the driving force distribution to the wheels with superior stability and response while effectively utilizing the tire grip. Specifically, the present invention provides a vehicle motion control device for a vehicle, the vehicle having a plurality of wheels and a driving device for driving the wheels based on a driving force/load distribution ratio, having: a force detection unit for detecting forces that act on the wheels; a target distribution ratio calculating unit for obtaining nonlinear terms by use of a group of parameters including the forces detected by the force detection unit, and obtaining a target value of the driving force/load distribution ratio so as to minimize the nonlinear terms, the nonlinear terms being included in elements of a system matrix of equations of state that describe a state of motion of the vehicle; and a driving device control unit for controlling the driving device based on the target value of the driving force/load distribution ratio.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of copending U.S. patent applicationSer. No. 11/196,167 filed on Aug. 3, 2005. This application furtherclaims priority under 35 U.S.C. 119 based upon Japanese PatentApplication Serial No. 2004-227639, filed on Aug. 4, 2004, JapanesePatent Application Serial No. 2004-228431, filed on Aug. 4, 2004, andJapanese Patent Application Serial No. 2005-065624, filed on Mar. 9,2005. The entire disclosures of the aforesaid applications areincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to vehicle motion control devices andmethods, and, in particular, to devices and methods for controlling themotion of a vehicle through controlling the distribution ratio of thedriving force based on the forces that act on the wheels.

2. Description of the Related Art

Conventionally, there are known technologies for controlling the stateof motion of a vehicle through controlling the distribution ratio of thedriving force between the front and rear wheels and/or between the leftand right wheels.

The main objective of these technologies is to improve steering bycontrolling the driving force distribution ratio to achieve anappropriate state of motion of the vehicle under certain drivingconditions such as cornering. Japanese Patent Publication 3132190disclosed a device for controlling the state of motion of a vehicle bymeans of a wheel frictional force utilization ratio. In the device, thewheel frictional force utilization ratios are calculated for therespective wheels, which are then controlled so that the wheelfrictional force utilization ratios become close to the respectivetarget values.

Japanese Kokai Laid-open Publication H 11-102499 disclosed a methodwherein the state of motion of a vehicle is controlled by utilizing thefact that the vehicle behavior is affected by the elements in the systemmatrix of equations of state that describe the state of motion of thevehicle.

However, the main focus of the technologies described above is theeffective utilization of the driving force; thus, issues such asstability and response are not fully considered. In particular, if thewheel friction utilization ratio is controlled to the limit duringspinning, the control mechanism would rely heavily on the grip of thetires on the outer wheels, leading to problems such as the loss ofstability against disturbances due to, for example, a sudden change inthe friction coefficient with the road surface.

In other words, in the technologies described above, the nonlinearelements of the vehicle motion are not properly taken into considerationin controlling the vehicle behavior; as a result, there is a possibilitythat steering stability gets degraded.

The entire disclosures of Japanese Patent Publication 3132190 andJapanese Kokai Laid-open Publication H 11-102499 are incorporated hereinby reference.

SUMMARY OF THE INVENTION

In view of the above circumstances, the objective of the presentinvention is to provide a vehicle motion control device capable ofcontrolling the driving force distribution to the wheels with superiorstability and response while effectively utilizing the tire grip.

According to one aspect of the present invention, there is provided avehicle motion control device for a vehicle, the vehicle having aplurality of wheels and a driving device for driving the wheels based ona driving force/load distribution ratio, comprising: a force detectionunit for detecting forces that act on the wheels; a target distributionratio calculating unit for obtaining nonlinear terms by use of a groupof parameters including the forces detected by the force detection unit,and obtaining a target value of the driving force/load distributionratio so as to minimize the nonlinear terms, the nonlinear terms beingincluded in elements of a system matrix of equations of state thatdescribe a state of motion of the vehicle; and a driving device controlunit for controlling the driving device based on the target value of thedriving force/load distribution ratio.

In addition, there is provided a vehicle motion control method forcontrolling motion of a vehicle according to the above aspect of thepresent invention.

According to another aspect of the present invention, there is provideda vehicle motion control device for a vehicle, the vehicle having aplurality of wheels and a driving device for driving the wheels based ona driving force/load distribution ratio, comprising: a calculating unitfor obtaining, based on equations of state that describe a state ofmotion of the vehicle, a divergence value, which is a characteristicvalue that represents a tendency of vectors in a vector field, thevector field describing a state surface with axes representing statevariables for the state of motion of the vehicle; a setting unit forsetting a target value of the driving force/load distribution ratio forthe individual wheels, such that the divergence value becomes less thana current value of the divergence value or the divergence value becomesless than or equal to zero; and a driving device control unit forcontrolling the driving device based on the target driving force/loaddistribution ratio.

In addition, there is provided a vehicle motion control method forcontrolling motion of a vehicle according to the above another aspect ofthe present invention.

According to yet another aspect of the present invention, there isprovided a vehicle motion control device for a vehicle, the vehiclehaving a plurality of wheels and a driving device for driving the wheelsbased on a driving force/load distribution ratio, comprising: acalculating unit for obtaining, based on equations of state thatdescribe a state of motion of the vehicle, a damping value, which is acharacteristic value that represents a convergence of the vehicle as anoscillator system; a setting unit for setting a target value of thedriving force/load distribution ratio for the individual wheels, suchthat the damping value becomes larger than a current value of thedamping value; and a driving device control unit for controlling thedriving device based on the target value of the driving force/loaddistribution ratio.

In addition, there is provided a vehicle motion control method forcontrolling motion of a vehicle according to the above aspect of theinvention.

Those skilled in the art will appreciate these and other advantages andbenefits of various embodiments of the invention upon reading thefollowing detailed description of the preferred embodiments withreference to the below-listed drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic structural diagram of a driving force distributioncontrol device according to the first example of a first embodiment ofthe present invention.

FIG. 2 is a skeleton diagram showing the schematic structure of a frontwheel final velocity reduction device.

FIG. 3 is an explanatory diagram showing the two-wheel drive modelequivalent to a four-wheel drive vehicle.

FIG. 4 is an explanatory diagram showing, functionally, the equations ofstate of motion for the two-wheel drive model.

FIG. 5 is a schematic structural diagram of a driving force distributioncontrol device according to the second example of the first embodimentof the present invention.

FIG. 6 is a schematic structural diagram of a driving force distributioncontrol device according to the third example of the first embodiment ofthe present invention.

FIG. 7 is an explanatory diagram showing the two-wheel drive model.

FIG. 8 is a block diagram showing the equations of state for vehiclemotion.

FIG. 9 is an explanatory diagram showing the forces acting on a vehicle.

FIG. 10 is a graph showing the trends in the driving force distributionratios that minimize the nonlinear term in the element a11.

FIG. 11 is a graph showing the trends in the driving force distributionratios that minimize the nonlinear terms in the elements a12 and a21.

FIG. 12 is a graph showing the trends in the driving force distributionratios that minimize the nonlinear term in the element a22.

FIG. 13 is a block diagram illustrating the overall structure of avehicle motion control device.

FIG. 14 is a block diagram showing the process flow of the vehiclemotion control device.

FIG. 15 is a flowchart showing the procedures according to the vehiclemotion control.

FIG. 16 is an explanatory diagram showing a state surface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention are described below with referenceto the accompanying drawings to facilitate understanding of the presentinvention.

Note that a first through ninth embodiments are described below: in somecases, an identical variable is referred to by using different notationsbetween in the first embodiment and the other embodiments. Therefore,the notations used in the first embodiment are valid only within thefirst embodiment; and the notations used in the other embodiment arevalid only within those embodiments.

First Embodiment

A first example of a first embodiment according to the present inventionis described below with reference to the accompanying drawings. FIG. 1is a schematic diagram of a driving force distribution control device,FIG. 2 is a skeleton diagram showing the schematic structure of a frontwheel final velocity reduction device, FIG. 3 is an explanatory diagramshowing an equivalent two-wheel vehicle model for a 4-wheel vehicle, andFIG. 4 is an explanatory diagram showing the equations of motionfunctionally based on the vehicle motion model.

In FIG. 1, the reference numeral 1 indicates a vehicle such as anautomobile. In the present embodiment, the vehicle 1 is a front wheeldrive automobile, where a driving force generated by an engine 2 istransmitted through a torque converter 3 and a transmission 4 to atransmission output axle 4 a. The driving force transmitted to thetransmission output axle 4 a is further transmitted through a reductiongear array 5 to a drive axle (front drive axle) 9, and inputted to afront wheel final velocity reduction device 10. The driving force thatis inputted to the front wheel final velocity reduction device 10 isfurther transmitted to left and right front wheels 12 fl and 12 fr,which are the drive wheels, through front wheel left and right axles 11fl and 11 fr, which are the drive axles.

Here the front wheel final velocity reduction device 10 has variablecontrol of the distribution ratio of the driving force between the leftand right front wheels 12 fl and 12 fr.

Specifically, the front wheel final velocity reduction device 10, asshown in FIG. 2, comprises a differential system 20, a gear system 21,and a clutch system 22.

The differential system 20 comprises, for example, a bevel gear-typedifferential system. A final gear 26, which engages with a drive pinion9 a of the front drive axle 9, is housed in a differential case 25 ofthe differential system 20. Moreover, in the differential case 25, apair of differential pinions 27 are rotatably held around an axis, andthe front wheel left and right axles 11 fl and 11 fr are connected toleft and right side gears 28 l and 28 r that engage with the pair ofdifferential pinions 27.

The gear system 21 comprises first and second gears 30 and 31, rigidlyattached to the front wheel right axle 11 fr, third and fourth gears 32and 33, rigidly attached to the front wheel left axle 11 fl, and 5th-8thgears 34-37, which engage, respectively, therewith. In the presentembodiment, the second gear 31 has a larger diameter than the first gear30, and the number of gear teeth z2 of the second gear 31 is larger thanthe number of gear teeth z1 of the first gear 30. Furthermore, the thirdgear 32 has the same diameter as the first gear 30 (where the number ofgear teeth z3=z1), and the fourth gear 33 has the same diameter as thesecond gear 31 (where the number of gear teeth z4=z2). The 5th-8th gears34-37 are arrayed on a single axis of rotation, parallel to the frontwheel axles 11 fl and 11 fr. The first and 5th gears 30 and 34 comprisea first gear array by engaging with each other, where the number of gearteeth z5 of the 5th gear 34 is set so that the first gear array gearratio (z5/z1) is, for example, 1.0. The second and 6th gears 31 and 35comprise a second gear array by engaging with each other, where thenumber of gear teeth z6 of the 6th gear is set so that the second geararray gear ratio (z6/z2) is, for example, 0.9. The 3rd and 7th gears 32and 36 comprise a 3rd gear array by engaging with each other, where thenumber of gear teeth z7 of the 7th gear is set so that the 3rd geararray gear ratio (z7/z3) is, for example, 1.0. The 4th and 8th gears 33and 37 comprise a fourth gear array by engaging with each other, and thenumber of gear teeth z8 of the 8th gear is set so that the 4th geararray gear ratio (z8/z4) is, for example, 0.9.

The clutch system 22 comprises a first hydraulic multi-board clutch 38that connects detachably the 5th gear 34 and the 8th gear 37, and asecond hydraulic multi-board clutch 39 that connects detachably the 6thgear 35 and the 7th gear 36. A hydraulic operation control unit 51 (seeFIG. 1) is connected to a hydraulic chamber (not shown) of each of thehydraulic multiple plate clutches 38 and 39, where the hydraulicpressure supplied from the hydraulic operation control unit 51distributes most of the driving force to the front wheel left axle 11 flwhen the first hydraulic multi-board clutch 38 is engaged, or, on theother hand, distributes most of the driving force to the front wheelright axle 11 fr when the second hydraulic multi-board clutch 39 isengaged.

Here the hydraulic pressure values for engaging the respective hydraulicmulti-board clutches 38 and 39 are calculated by the hydraulic operationcontrol unit 51 according to the driving force distribution ratiobetween the left and right front wheels 12 fl and 12 fr, set by adriving force distribution ratio setting unit 50 (described below). Thedriving force distribution ratio setting unit 50 is a driving forcedistribution ratio setting means in the present embodiment, wherein theamount of torque distribution (the amount of the driving forcedistributed) can be varied according to the hydraulic pressure values.In other words, the hydraulic operation control unit 51 performs afunction as a driving force distribution means, along with the frontwheel final velocity reduction device 10. Note that the structure ofthis type of final velocity reduction devices is described in detail in,for example, Japanese Kokai Laid-open Publication H 11-263140, and isnot limited to the structure described in the present embodiment. Theentire disclosure of Japanese Kokai Laid-open Publication H 11-263140 isincorporated herein by reference.

As is shown in FIG. 1, the driving force distribution ratio setting unit50 is connected to force detecting sensors 14 fl and 14 fr, a roadsurface friction coefficient estimating unit 53, and a longitudinaldriving force calculating unit 54. The force detecting sensors 14 fl and14 fr serve as a force detecting means for detecting the forces appliedto the drive wheels (the left and right front wheels 12 fl and 12 fr).

In the present embodiment, the force detecting sensors 14 fl and 14 frare embedded in axle housings 13 fl and 13 fr of the left and rightfront wheels 12 fl and 12 fr, where at least the lateral forces (thefront wheel lateral forces Ffl_y and Ffr_y) and the vertical forces (thefront wheel vertical forces Ffl_z and Ffr_z), acting on the wheels 12 fland 12 fr, respectively, are detected based on the differential amountgenerated in the axle housings 13 fl and 13 fr.

The road surface friction coefficient estimating unit 53 comprises, forexample, an ABS (antilock brake system) control unit, and calculates theroad surface friction coefficient μ (hereinafter termed also the roadsurface μ) using, for example, the estimation method proposed by thepresent applicants in Japanese Kokai Laid-open Publication H 8-2274. Inthe road surface friction coefficient estimating unit 53, a corneringpower of the wheels is estimated by extrapolating to the non-linearregion the equation of lateral motion described with a front wheelsteering angle 8 f, a vehicle velocity V, and an actual yaw rate (dφ/dt)inputted from a steering sensor 60, a vehicle velocity sensor 61, and ayaw rate sensor 62, respectively; and the road surface frictioncoefficient μ is estimated by using a ratio between the estimatedcornering power and a cornering power equivalent to the case of μ=1.0(high μ road) for each of the front and rear wheels. Note that theestimation method is not limited to the above approach. For example, themethod disclosed by the present applicants in Japanese Kokai Laid-openPublication 2000-71968 may be employed. The entire disclosures ofJapanese Kokai Laid-open Publications H 8-2274 and 2000-71968 areincorporated herein by reference.

The longitudinal driving force calculating unit 54 comprises, forexample, an engine control unit, and calculates, for example, an enginedriving force Fe as the longitudinal driving force (driver-requesteddriving force) Fx. In other words, an engine rotation number Ne, aturbine rotation number Nt, and a throttle opening angle θth areinputted into the longitudinal driving force calculating unit 54 from anengine rotation number sensor 63, a turbine rotation number sensor 64,and a throttle opening angle sensor 62. Also inputted is a currenttransmission gear ratio rg from a transmission control unit 66. By usingthese inputs, the engine driving force Fe is calculated as in Eq. (1):

$\begin{matrix}{{Fe} = \frac{{Tt} \cdot {rf}}{Rw}} & (1)\end{matrix}$

where rf is a final gear ratio, RW is an effective radius of a tire, andTt is a torque after the transmission gear is applied. By using anengine torque Te, a conversion ratio of the torque converter tconv, anda dynamical transmission efficiency η, Tt is expressed as in Eq. (2):

Tt=Te·rg·tconv·η  (2)

where the engine torque Te is obtained from a map based on the enginerotation number Ne and the throttle opening angle θth; and the torqueconversion ratio tconv is obtained from a map based on a velocity ratiorv (=Nt/Ne) of the torque converter.

Using front and rear wheel cornering forces (per wheel) Ff and Fr, amass of the vehicle M, and a lateral acceleration (d²y/dt²) in thevehicle motion model in FIG. 3, the equation of motion related to thetranslational motion in the lateral direction of the vehicle is given byEq. (3):

$\begin{matrix}{{M \cdot \frac{^{2}y}{t^{2}}} = {{2{Ff}} + {2 \cdot {Fr}}}} & (3)\end{matrix}$

On the other hand, using the distances from the center of mass to thefront and rear wheel axles if and lr, a moment of inertia of the vehicleIz, and a yaw angular acceleration (d²φ/dt²), the equation of motionpertaining to the rotational movement about the center of mass is givenby Eq. (4):

$\begin{matrix}{{{Iz} \cdot \frac{^{2}\varphi}{t^{2}}} = {{2 \cdot {Fr} \cdot {lf}} - {2{{Fr} \cdot {lr}}}}} & (4)\end{matrix}$

Moreover, using a vehicle sliding angle β and a vehicle sliding angularvelocity (dβ/dt), the lateral acceleration (d²y/dt²) is expressed as inEq. (5):

$\begin{matrix}{\frac{^{2}y}{t^{2}} = {V \cdot \left( {\frac{\beta}{t} + \frac{\varphi}{t}} \right)}} & (5)\end{matrix}$

Using front and rear wheel equivalent cornering powers Kf and Kr andfront and rear wheel lateral sliding angles βf and βr, the front andrear wheel average cornering forces Ff_y and Fr_y are expressed asfollows:

$\begin{matrix}{{Ff\_ y} = {{{{Kf} \cdot \beta}\; f} - \frac{{{Kf}^{2} \cdot \beta}\; f^{2}}{4 \cdot {Ff\_ yMAX}}}} & (6) \\{{Fr\_ y} = {{{{Kr} \cdot \beta}\; r} - \frac{{{Kr}^{2} \cdot \beta}\; r^{2}}{4 \cdot {Fr\_ yMAX}}}} & (7)\end{matrix}$

The actual front and rear wheel cornering powers Kf_a and Kr_a are givenby the following equations:

$\begin{matrix}{{Ff\_ a} = {\frac{\partial{Ff\_ y}}{{\partial\beta}\; f} = {{Kf} - \frac{{Kf}^{2} \cdot {{\beta \; f}}}{2 \cdot {Ff\_ yMAX}}}}} & (8) \\{{Fr\_ a} = {\frac{\partial{Fr\_ y}}{{\partial\beta}\; r} = {{Kr} - \frac{{Kr}^{2} \cdot {{\beta \; r}}}{2 \cdot {Fr\_ yMAX}}}}} & (9)\end{matrix}$

Here, using the front and rear wheel average longitudinal forces Ff_xand Fr_x and the front and rear wheel average vertical forces Ff_z andFr_z, Ff_y MAX and Fr_y MAX in the above equations are expresses asfollows:

$\begin{matrix}{{Ff\_ yMAX} = \left( {{\mu^{2} \cdot {Ff\_ z}^{2}} - {Ff\_ x}^{2}} \right)^{\frac{1}{2}}} & (10) \\{{Ff\_ yMAX} = \left( {{\mu^{2} \cdot {Fr\_ z}^{2}} - {Fr\_ x}^{2}} \right)^{\frac{1}{2}}} & (11)\end{matrix}$

Moreover, by use of the front wheel steering angle δf, the front andrear wheel lateral sliding angles βf and βr can be simplified asfollows:

$\begin{matrix}{{\beta \; f} = {\beta + {{lf} \cdot \frac{\frac{\varphi}{t}}{V}} - {\delta \; f}}} & (12) \\{{\beta \; r} = {\beta + {{lr} \cdot \frac{\frac{\varphi}{t}}{V}}}} & (13)\end{matrix}$

The equations of motion described above lead to the equations of statefor obtaining the vehicle sliding angle β and the yaw rate (dφ/dt),using the steering angle δf as the input, as shown below:

$\begin{matrix}{\begin{bmatrix}\frac{\beta}{t} \\\frac{^{2}\varphi}{t^{2}}\end{bmatrix} = {{\begin{bmatrix}{{- a}\; 11} & {{- a}\; 12} \\{{- a}\; 21} & {{- a}\; 22}\end{bmatrix}\begin{bmatrix}\beta \\\frac{\varphi}{t}\end{bmatrix}} + {\begin{bmatrix}{b\; 1} & 0 \\{b\; 2} & 0\end{bmatrix}\begin{bmatrix}{\delta \; f} \\0\end{bmatrix}}}} & (14) \\{{a\; 11} = {2 \cdot \frac{{kf\_ a} + {kr\_ a}}{M \cdot V}}} & (15) \\{{a\; 12} = {1 + {2 \cdot \frac{{{lf} \cdot {kf\_ a}} - {{lr} \cdot {kr\_ a}}}{M \cdot V^{2}}}}} & (16) \\{{a\; 21} = {2 \cdot \frac{{{lf} \cdot {kf\_ a}} - {{lr} \cdot {kr\_ a}}}{Iz}}} & (17) \\{{a\; 22} = {2 \cdot \frac{{{lf}^{2} \cdot {kf\_ a}} - {{lr}^{2} \cdot {kr\_ a}}}{{Iz} \cdot V}}} & (18) \\{{b\; 1} = {2 \cdot \frac{kf\_ a}{M \cdot V}}} & (19) \\{{b\; 2} = {2 \cdot {lf} \cdot \frac{kf\_ a}{Iz}}} & (20)\end{matrix}$

The relationships among these parameters are shown in FIG. 4.

Here, in Eq. (14), the contribution of the a11 term to the convergenceof the vehicle sliding angle is well known: the more linearly this termvaries, the greater the stability of the vehicle, and greater thefeeling of responsiveness experienced by the driver. Let the left frontwheel longitudinal force be Ffl_x, the right front wheel longitudinalforce be Ffr_x, the left rear wheel longitudinal force be Frl_x, theright rear wheel longitudinal force be Frr_x, the left front wheelvertical force be Ffl_z, the right front wheel vertical force be Ffr_z,the left rear wheel vertical force be Frl_z, and the right rear wheelvertical force be Frr_z, using Eqs. (8)-(11), then the a11 term can beexpanded in terms of the cornering powers kfl_a, kfr_a, krl_a and krr_aof each of the wheels as follows:

$\begin{matrix}\begin{matrix}{{a\; 11} = \frac{{kfl\_ a} + {kfr\_ a} + {krl\_ a} + {krr\_ a}}{M \cdot V}} \\{= {\frac{1}{M \cdot V} \cdot}} \\{\begin{bmatrix}{{2 \cdot \left( {{Kf} + {Kr}} \right)} - {\frac{1}{2} \cdot \begin{bmatrix}{\frac{{Kf}^{2}}{\left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {Ffl\_ x}^{2}} \right)^{\frac{1}{2}}} +} \\\frac{{Kf}^{2}}{\left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {Ffr\_ x}^{2}} \right)^{\frac{1}{2}}}\end{bmatrix} \cdot {{\beta \; f}}} - {\frac{1}{2} \cdot}} \\{{\begin{bmatrix}{\frac{{Kr}^{2}}{\left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {Frl\_ x}^{2}} \right)^{\frac{1}{2}}} +} \\\frac{{Kr}^{2}}{\left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {Frr\_ x}^{2}} \right)^{\frac{1}{2}}}\end{bmatrix} \cdot {{\beta \; r}}}}\end{bmatrix}}\end{matrix} & (21)\end{matrix}$

When the front and rear wheel lateral sliding angles βf and βr aresufficiently small, the following approximations can be obtained:Kf·|βf|=Ffl_y|=|Ffr_y| (where Ffl_y is the left front wheel lateralforce and Ffr_y is the right front wheel lateral force), andKr·|βr|=|Frl_y|=|Frr_y| (where Frl_y is the left rear wheel lateralforce and Frr_y is the right rear lateral force). Using theseapproximations, Eq. (21) can be rewritten as follows:

$\begin{matrix}{{a\; 11} = {\frac{1}{M \cdot V} \cdot {\quad\begin{bmatrix}{{2 \cdot \left( {{Kf} + {Kr}} \right)} - {\frac{1}{2} \cdot \begin{bmatrix}{{{Kf} \cdot \frac{{Ffl\_ y}}{\left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {Ffl\_ x}^{2}} \right)^{\frac{1}{2}}}} + {{Kf} \cdot}} \\\frac{{Ffr\_ y}}{\left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {Ffr\_ x}^{2}} \right)^{\frac{1}{2}}}\end{bmatrix}} -} \\{\frac{1}{2} \cdot \begin{bmatrix}{{{Kr}\frac{{Frl\_ y}}{\left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {Frl\_ x}^{2}} \right)^{\frac{1}{2}}}} +} \\{{Kr}\frac{{Frr\_ y}}{\left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {Frr\_ x}^{2}} \right)^{\frac{1}{2}}}}\end{bmatrix}}\end{bmatrix}}}} & (22)\end{matrix}$

In the following, a front/rear driving force distribution ratio isdenoted by a (where 0≦a≦1), a front wheel right/left driving forcedistribution ratio is denoted by b (where 0≦b≦1), and a rear wheelright/left driving force distribution ratio is denoted by c (where0≦c≦1). Then the driving force for each of the wheels 12 fl, 12 fr, 12rl, and 12 rr (denoted by Ffl_x, Ffr_x, Frl_x and Frr_x) is expressed interms of a driver-requested driving force Fx as follows:

Ffl _(—) x=a·b·Fx  (23)

Ffr _(—) x=a·(1−b)·Fx  (24)

Frl _(—) x=(1−a)·c·Fx  (25)

Frr _(—) x=(1−a)·(1−c)·Fx  (26)

Substituting these expressions into Eq. (22) leads to the following:

$\begin{matrix}{{a\; 11} = {\frac{1}{M \cdot V} \cdot {\quad\begin{bmatrix}{{2 \cdot \left( {{Kf} + {Kr}} \right)} - {\frac{1}{2} \cdot \begin{bmatrix}{{{Kf} \cdot \frac{{Ffl\_ y}}{\left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {a^{2} \cdot b^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}}} +} \\{{Kf} \cdot \frac{{Ffr\_ y}}{\begin{pmatrix}{{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {a^{2} \cdot}} \\{\left( {1 - b} \right)^{2} \cdot {Fx}^{2}}\end{pmatrix}^{\frac{1}{2}}}}\end{bmatrix}} -} \\{\frac{1}{2} \cdot \begin{bmatrix}{{{Kr}\frac{{Frl\_ y}}{\left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot c^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}}} +} \\{{Kr}\frac{{Frr\_ y}}{\begin{pmatrix}{{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {\left( {1 - a} \right)^{2}{\left( {1 - c} \right)^{2} \cdot}}} \\{Fx}^{2}\end{pmatrix}^{\frac{1}{2}}}}\end{bmatrix}}\end{bmatrix}}}} & (27)\end{matrix}$

In Eq. (27), the terms inside the braces [ ] are dependent on the frontand rear wheel cornering powers Kf_a and Kr_a. Using the followingrelationships:

2·Ff _(—) x=a·Fx  (28)

2·Fr _(—) x=(1−a)·Fx  (29)

the front and rear wheel cornering powers Kf_a and Kr_a are extractedfrom Eq. (27) as follows:

$\begin{matrix}\begin{matrix}{{kf\_ a} = {{Kf} - \frac{{Kf} \cdot {{Ffl\_ y}}}{4 \cdot \left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {a^{2} \cdot b^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}} -}} \\{\frac{{Kf} \cdot {{Ffr\_ y}}}{4 \cdot \left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {a^{2} \cdot \left( {1 - b} \right)^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}}} \\{= {{Kf} - \frac{{Kf} \cdot {{Ffl\_ y}}}{4 \cdot \left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {4 \cdot b^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}} -}} \\{\frac{{Kf} \cdot {{Ffr\_ y}}}{4 \cdot \left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {a^{2} \cdot 4 \cdot \left( {1 - b} \right)^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}}}\end{matrix} & (30) \\\begin{matrix}{{kr\_ a} = {{Kr} - \frac{{Kr} \cdot {{Frl\_ y}}}{4 \cdot \left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot c^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}} -}} \\{\frac{{Kr} \cdot {{Frr\_ y}}}{4 \cdot \left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot \left( {1 - c} \right)^{2} \cdot {Fx}^{2}}} \right)^{\frac{1}{2}}}} \\{= {{Kr} - \frac{{Kr} \cdot {{Frl\_ y}}}{4 \cdot \left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {4 \cdot c^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}} -}} \\{\frac{{Kr} \cdot {{Frr\_ y}}}{4 \cdot \left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {4 \cdot \left( {1 - c} \right)^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}}}\end{matrix} & (31)\end{matrix}$

As seen clearly from Eqs. (30) and (31), for the case of a front-wheeldrive vehicle with the front/rear driving force distribution ratio a=1,it is possible to minimize the nonlinear term of a11 in Eq. (27) byobtaining the front wheel right/left driving force distribution ratio bthat minimizes the nonlinear term of the front wheel cornering powerkf_a. Based on this fact, in the driving force distribution ratiosetting unit 50, the front wheel right/left driving force distributionratio b is obtained so as to minimize the nonlinear term of the frontwheel cornering power Kf_a:

$\begin{matrix}{{{Non}\; {linear}\mspace{14mu} {term}} = {\frac{{Kf} \cdot {{Ffl\_ y}}}{4 \cdot \left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {4 \cdot b^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}} + \frac{{Kf} \cdot {{Ffr\_ y}}}{4 \cdot \left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {4 \cdot \left( {1 - b} \right)^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}}}} & (32)\end{matrix}$

and this front wheel right/left driving force distribution ratio b isset as the control value for the distribution ratio when transmittingthe driving force 2·Ff_x(=a·Fx) from the front wheel final velocityreduction device 10 to the front wheel left and right axles 11 fl and 11fr.

Specifically, in the driving force distribution ratio setting unit 50,the front wheel lateral force Ffl_y and front wheel vertical forceFfl_z, detected by the force detecting sensor 14 fl, are substituted forFfl_y and Ffl_z in Eq. (32), and the front wheel lateral force Ffr_y andfront wheel vertical force Ffr_z, detected by the force detecting sensor14 fr, are substituted for Ffr_y and Ffr_z in Eq. (32). Moreover, byassuming that the road surface μ acting on each wheel is identical, theroad surface μ estimated by the road surface friction coefficientestimating unit 53 is substituted for μfl and μfr in Eq. (32), and thedriving force Fx calculated by the longitudinal driving forcecalculating unit 54 is substituted for Ff_x (=Fx/2) in Eq. (32).

Thereafter, by inputting, sequentially b=0.0, 0.1, . . . 0.9, 1.0, forexample, into b in Eq. (32), the driving force distribution ratiosetting unit 50 proceeds to find the front wheel right/left drivingforce distribution ratio b that minimizes the nonlinear term of thefront wheel cornering power Kf_a.

Therefore, as seen above, it is possible to set a driving forcedistribution ratio that provides superior stability to disturbancesthrough effective utilization of the tire grip by minimizing thenonlinear term in the cornering power, which is anticipated to actuallybe generated at vehicle wheels.

Moreover, because the driving force distribution control causes thechange in the cornering power generated at the vehicle wheels toapproach a linear variation, it is possible to improve the response, andto thereby operate the vehicle with the feeling of being in the normaldomain even when the tires approach the nonlinear domain.

Furthermore, because the wheel's lateral force and vertical force,obtained directly from the force detecting sensors, are used inestimating the cornering power, it is possible to achieve driving forcedistribution control with excellent precision according to actualvehicle behavior.

Next, FIG. 5 is a schematic structural diagram of a driving forcedistribution control device according to a second example of the presentfirst embodiment. This example describes the case wherein the rear wheelright/left driving force distribution ratio c is set by the drivingforce distribution ratio setting unit 50. Note that the explanations ofnotations are omitted for structural elements that are identical tothose in the first example of the present embodiment.

As is shown in FIG. 5, the driving force generated by the engine 2 inthe present example is transmitted through the torque converter 3 andthe transmission 4 to the transmission output axle 4 a. The drivingforce transmitted to the transmission output axle 4 a is furthertransmitted through a propeller shaft 16 to a drive pinion axle 17, andis inputted to a rear wheel final velocity reduction device 18. Thedriving force inputted to the rear wheel final velocity reduction device18 is further transmitted to the left and right rear wheels 12 rl and 12rr, which are the drive wheels, through the rear wheel left and rightaxles 11 rl and 11 rr, which are the drive axles.

Here the rear wheel final velocity reduction device 18 has variablecontrol of the distribution ratio of the driving force that istransmitted to the left and right rear wheels 12 rl and 12 rr.Specifically, the rear wheel final velocity reduction device 18 isstructured in essentially the same way as the front wheel final velocityreduction device 10 shown in FIG. 2 in the first example of the presentembodiment. In this case, with respect to the rear wheel final velocityreduction device 18, the drive pinion axle 17 corresponds to the frontdrive axle 9 shown in FIG. 2, and the rear wheel left and right axles 11rl and 11 rr correspond to the front wheel left and right axles 11 fland 11 fr shown in FIG. 2.

Here, in the rear wheel final velocity reduction device 18, thehydraulic pressure values for engaging the respective hydraulicmulti-board clutches 38 and 39 are calculated by the hydraulic operationcontrol unit 51 according to the driving force distribution ratiobetween the left and right rear wheels 12 rl and 12 rr, set by thedriving force distribution ratio setting unit 50. The distributedamounts of the driving force can be varied according to these hydraulicpressure values. In other words, the hydraulic operation control unit 51performs a function as a driving force distribution means, along withthe rear wheel final velocity reduction device 18.

As is shown in FIG. 5, the force detecting sensors 14 rl and 14 rr areconnected to the driving force distribution ratio setting unit 50, andare force detecting means for detecting the forces applied to the wheels(the left and right rear wheels 12 rl and 12 rr). In the presentembodiment, the force detecting sensors 14 rl and 14 rr are embedded inthe axle housings 13 rl and 13 rr of the left and right rear wheels 12rl and 12 rr, and detect at least the forces in the lateral direction(rear wheel lateral forces Frl_y and Frr_y) and forces in the verticaldirection (rear wheel vertical forces Frl_z and Frr_z) that act uponeach of the wheels 12 rl and 12 rr, based on the differential amountgenerated in the axle housings 13 rl and 13 rr.

As seen clearly from Eqs. (30) and (31), for the case of a rear-wheeldrive vehicle with the front/rear driving force distribution ratio a=0,it is possible to minimize the nonlinear term of a11 in Eq. (27) byobtaining the rear wheel right/left driving force distribution ratio cthat minimizes the nonlinear term of the rear wheel cornering powerKr_a.

Based on this fact, in the driving force distribution ratio setting unit50, the rear wheel right/left driving force distribution ratio c isobtained so as to minimize the nonlinear term of the rear wheelcornering power Kr_a:

$\begin{matrix}{{{Non}\; {linear}\mspace{14mu} {term}} = {\frac{{Kr} \cdot {{Ffl\_ y}}}{4 \cdot \left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {4 \cdot c^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}} + \frac{{Kr} \cdot {{Frr\_ y}}}{4 \cdot \left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {4 \cdot \left( {1 - c}\; \right)^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}}}} & (33)\end{matrix}$

and this rear wheel right/left driving force distribution ratio c is setas the control value for the distribution ratio when transmitting thedriving force 2·Ff_x(=(1−a)·Fx) from the rear wheel final velocityreduction device 18 to the rear wheel left and right axles 11 rl and 11rr.

Specifically, in the driving force distribution ratio setting unit 50,the rear wheel lateral force Frl_y and rear wheel vertical force Frl_z,detected by the force detecting sensor 14 rl, are substituted for Frl_yand Frl_z in Eq. (33), and the rear wheel lateral force Frr_y and rearwheel vertical force Frr_z, detected by the force detecting sensor 14rr, are substituted for Frr_y and Frr_z in Eq. (33). Moreover, byassuming that the road surface μ acting on each wheel is identical, theroad surface μ estimated by the road surface friction coefficientestimating unit 53 is substituted for μrl and μrr in Eq. (33), and thedriving force Fx calculated by the longitudinal driving forcecalculating unit 54 is substituted for Ff_x (=Fx/2) in Eq. (33).

Thereafter, by inputting, sequentially c=0.0, 0.1, . . . 0.9, 1.0, forexample, into c in Eq. (33), the driving force distribution ratiosetting unit 50 proceeds to find the rear wheel right/left driving forcedistribution ratio c that minimizes the nonlinear term of the rear wheelcornering power Kr_a.

According to the above second example of the present embodiment, it ispossible to achieve the same effect as in the first example for the rearwheel driving force distribution control.

Next, FIG. 6 is a schematic structural diagram of a driving forcedistribution control device according to a third example of the presentfirst embodiment. This example describes the case wherein the front/rearwheel driving force distribution ratio a is set by the driving forcedistribution ratio setting unit 50. Note that the explanations ofnotations are omitted for structural elements that are identical tothose in the first or second example of the present embodiment.

As shown in FIG. 6, the driving force generated by the engine 2 in thepresent example is transmitted through the torque converter 3, thetransmission 4, and the transmission output axle 4 a to a centerdifferential device 19. The driving force transmitted to the centerdifferential device 19 is further transmitted through the rear driveaxle 15, the propeller shaft 16, and the drive pinion axle 17, and isinputted to the rear wheel final velocity reduction device 18, as wellas transmitted thorough the front drive axle 9 to the front wheel finalvelocity reduction device 10.

Here, the center differential device 19 has variable control of thedistribution ratio of the driving force that is transmitted to the frontdrive axle 9 and the rear drive axle 15, which are drive axles.Specifically, the center differential device 19 is structured inessentially the same way as the front wheel final velocity reductiondevice 10 shown in FIG. 2 in the first example of the presentembodiment. In this case, with respect to the center differential device19, the transmission output axle 4 a corresponds to the front drive axle9 shown in FIG. 2, the front drive axle 9 corresponds to the front wheelright axle 11 fr shown in FIG. 2, and the rear drive axle 15 correspondsto the front wheel left axle 11 fl shown in FIG. 2.

Here, in the center differential device 19, the hydraulic pressurevalues for engaging the respective hydraulic multi-board clutches 38 and39 are calculated by the hydraulic operation control unit 51 accordingto the driving force distribution ratio between the front and rearwheels, set by the driving force distribution ratio setting unit 50. Thedistributed amounts of the driving force can be varied according tothese hydraulic pressure values. In other words, the hydraulic operationcontrol unit 51 performs a function as a driving force distributionmeans, along with the center differential device 19.

As shown in FIG. 6, the force detecting sensors 14 fl, 14 fr, 14 rl, and14 rr are connected to the driving force distribution ratio setting unit50, and are force detecting means for detecting the forces applied onthe wheels (the left and right front wheels 12 fl and 12 fr, and theleft and right rear wheels 12 rl and 12 rr).

In the present example, the driving force distribution ratios b and care assumed to be b=c=½, and the front/rear driving force distributionratio a is obtained so as to minimize the nonlinear terms in Eqs. (30)and (31). In other words, using the following relationships:

Front wheel average lateral force=Ff_(—) y(=Ffl _(—) y+Ffr _(—) y)/2),

Rear wheel average lateral force=Fr_(—) y(=Frl _(—) y+Frr _(—) y)/2),

Front wheel average vertical force=Ff_(—) z(=Ffl _(—) z+Ffr _(—) z)/2),and

Rear wheel average vertical force=Fr_(—) z(=Frl _(—) z+Frr _(—) z)/2),

the nonlinear term of the four wheel cornering power Kfr_a(=Kf_a+Kr_a)can be expressed as:

$\begin{matrix}{{{Nonlinear}\mspace{14mu} {term}} = {{\frac{{Kf} \cdot {{Ffl\_ y}}}{4 \cdot \left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {a^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}} + \frac{{Kf} \cdot {{Ffr\_ y}}}{4 \cdot \left( {{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {a^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}} + \frac{{Kr} \cdot {{Frl\_ y}}}{4 \cdot \left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}} + \frac{{Kr} \cdot {{Frr\_ y}}}{4 \cdot \left( {{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}}} \approx {{{Kf} \cdot \frac{{Ff\_ y}}{2 \cdot \left( {{\mu \; {f^{2} \cdot {Ff\_ z}^{2}}} - {a^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}}} + {{Kr} \cdot \frac{{Fr\_ y}}{2 \cdot \left( {{\mu \; {r^{2} \cdot {Fr\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}}}}}} & (34)\end{matrix}$

where,

Ffl_y≈Ffr_y≈Ff_y,Frl_y≈Frr_y≈Fr_y

Ffl_z≈Ffr_z≈Ff_z,Frl_z≈Frr_z≈Fr_z.

In the driving force distribution ratio setting unit 50, the rear/frontdriving force distribution ratio a that minimizes Eq. (34) is obtainedby essentially the same process as in the first and second examples, andthis driving force distribution ratio is set as the control value forthe distribution ratio when transmitting the driving force Fx from thecenter differential device 19 to the front drive axle 9 and the reardrive axel 15.

Moreover, in the driving force distribution ratio setting unit 50, thefront wheel driving force Ff_x and the rear wheel driving force Fr_x,obtained based on the set driving force distribution ratio a, can bothbe used to set the front wheel right/left driving force distributionratio b and the rear wheel right/left driving force distribution ratioc. Specifically, although in the first and second examples, some of thedistribution ratios were set to be 1 or 0, the values calculated asabove may be used to obtain the driving force distribution ratio a thatminimizes the nonlinear terms in the front wheel cornering power Kf_aand the rear wheel cornering power Kr_a.

According to this example of the present embodiment, it is possible toprovide essentially the same effect as in the first example even fordriving force distribution control for all four wheels, includingcontrolling the driving force distribution to the front and rear wheels.Note that in this case, instead of the tire lateral forces Ffl_y, Ffr_y,Frl_y and Frr_y, the tire sliding angles βf and βr for the front andrear wheels, obtained from Eqs. (12) and (13), may be used to obtain thefollowing nonlinear terms:

$\begin{matrix}{{{Nonlinear}\mspace{14mu} {term}} = {\frac{{Kf}^{\mspace{11mu} 2} \cdot {{\beta \; f}}}{4 \cdot \left( {{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {4 \cdot b^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}} + \frac{{Kf}^{\mspace{11mu} 2} \cdot {{\beta \; f}}}{4 \cdot \left( {{\mu \; f\; {r \cdot {Ffr\_ z}^{2}}} - {4 \cdot \left( {1 - b} \right)^{2} \cdot {Ff\_ x}^{2}}} \right)^{\frac{1}{2}}}}} & \left( 32^{\prime} \right) \\{{{Nonlinear}\mspace{14mu} {term}} = {\frac{{Kr}^{\mspace{11mu} 2} \cdot {{\beta \; r}}}{4 \cdot \left( {{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {4 \cdot c^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}} + \frac{{Kr}^{\mspace{11mu} 2} \cdot {{\beta r}}}{4 \cdot \left( {{\mu \; r\; {r \cdot {Frr\_ z}^{2}}} - {4 \cdot \left( {1 - c} \right)^{2} \cdot {Fr\_ x}^{2}}} \right)^{\frac{1}{2}}}}} & \left( 33^{\prime} \right) \\{{{Nonlinear}\mspace{14mu} {term}} = {{{Kf}^{\mspace{11mu} 2} \cdot \frac{{\beta \; f}}{2 \cdot \left( {{\mu \; {f^{2} \cdot {Ff\_ z}^{2}}} - {a^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}}} + {{Kr}^{2} \cdot \frac{{\beta \; f}}{2 \cdot \left( {{\mu \; {r^{2} \cdot {Fr\_ z}^{2}}} - {\left( {1 - a} \right)^{2} \cdot \frac{{Fx}^{2}}{4}}} \right)^{\frac{1}{2}}}}}} & \left( 34^{\prime} \right)\end{matrix}$

Note that the various equations including the linear terms and nonlinearterms representing the cornering powers, as well as their variations andapproximations, are not limited to those described above.

Furthermore, although, in the three examples of the present embodiment,explanations were given for driving force distribution to the left andright wheels using an FF vehicle (front engine—front wheel drivevehicle), an FR vehicle (front engine—rear wheel drive vehicle), and afour-wheel drive vehicle, respectively, the present invention is notlimited thereto. For example, in the case of a four-wheelindependent-motor driven vehicle which is equipped with four independentmotors to provide driving forces to respective wheels, it is possible toapply the present invention to control the left and right wheel motordriving forces or four-wheel motor driving forces. In this case, thecalculation and control units for obtaining the driving forces for therespective wheels correspond to the vehicle driving force distributioncontrol means.

Second Embodiment

Prior to describing the system structure and system processes regardingthe vehicle motion control device according to a second embodiment,first the system matrix in the equations of state is explained below inorder to define the control concept. Note that the braking force can beviewed as the reverse-direction component (the negative component) ofthe driving force, and thus the “driving force” in the presentembodiment is defined to include the braking force.

FIG. 7 is an explanatory diagram of a vehicle model. The vehicle modelshown in this figure is a two-wheel model to represent the state ofmotion of the vehicle in terms of a front wheel and a rear wheel. Inthis vehicle model, the state of motion of the vehicle is expressed interms of the rotational motion (the yaw motion) around the vertical axis(the Z axis), and the translational motion in the lateral direction (theY axis). When the front wheel is steered (and the rear wheel is parallelto the X axis), the state of motion of the vehicle is expressed by thefollowing equations of state:

$\begin{matrix}{\begin{bmatrix}{\beta \; b^{\prime}} \\\gamma^{\prime}\end{bmatrix} = {{\begin{bmatrix}{{- a}\; 11} & {{- a}\; 12} \\{{- a}\; 21} & {{- a}\; 22}\end{bmatrix}\begin{bmatrix}{\beta \; b} \\\gamma\end{bmatrix}} + {\begin{bmatrix}{b\; 1} & 0 \\{b\; 2} & 0\end{bmatrix}\begin{bmatrix}{\delta \; f} \\0\end{bmatrix}}}} & (35)\end{matrix}$

where βb is a vehicle body sliding angle (hereinafter referred to as abody sliding angle), γ is a yaw rate, and δf is a front wheel steeringangle. In the present application, the addition of an apostrophe symbolto any state variable indicates the derivative of that state variablewith respect to time. For example βb′ indicates a body sliding angularvelocity, which is the time derivative of the body sliding angle βb, andγ′ indicates an yaw angular acceleration, which is the time derivativeof the yaw rate γ. The equations of state in Eq. (35) are shown by theblock diagram in FIG. 8. This block diagram includes a block where theintegral (indicated by “1/s”) is an element, and shows the change ofthese equations of state (the state of motion of the vehicle) over time.

The system matrix for the equations has elements a11-a22 and b1 and b2,which are expressed as in Eq. (36):

$\begin{matrix}{{{a\; 11} = \frac{2\left( {{kf\_ a} + {kr\_ a}} \right)}{M \cdot V}}{{a\; 12} = {1 + \frac{2\left( {{{lf} \cdot {kf\_ a}} - {{lr} \cdot {kr\_ a}}} \right)}{M \cdot V^{2}}}}{{a\; 21} = \frac{2\left( {{{lf} \cdot {kf\_ a}} - {{lr} \cdot {kr\_ a}}} \right)}{Iz}}{{a\; 22} = \frac{2\left( {{{lf}^{\; 2} \cdot {kf\_ a}} + {{lr}^{2} \cdot {kr\_ a}}} \right)}{{Iz} \cdot V}}{{b\; 1} = \frac{2{kf\_ a}}{M \cdot V}}{{b\; 2} = \frac{2{{lf} \cdot {kf\_ a}}}{Iz}}} & (36)\end{matrix}$

where V is a velocity, M is a mass of the vehicle, if is the distancebetween the center of mass and the front wheel axle, lr is the distancebetween the center of mass and the rear wheel axle, Iz is a moment ofinertia of the vehicle around the Z axis of rotation, and ka is acornering power including nonlinearities of the vehicle wheels. Inaddition, kf_a denotes the cornering power ka of the front wheels, andkr_a denotes the cornering power of the rear wheels. For the case of afour-wheel vehicle, a quantity for the front wheels indicated by theletter “f” (or the rear wheels indicated by the letter “r”) can beregarded as the average of that for the left and right front wheels (orthe left and right rear wheels).

The cornering power ka is the rate of change of a cornering force withrespect to an infinitesimal change in a sliding angle of the wheel(hereinafter referred to as a wheel sliding angle) βw, where thecornering force is a component of a frictional force along the directionperpendicular to the direction of travel of the wheel, the frictionalforce being generated at the surface the wheel contracts during turningby the wheel sliding angle βw. That is, the cornering power ka is theslope (the derivative) of the cornering force at the wheel sliding angleβw. This cornering power ka is a parameter that has a large effect onthe stability of the vehicle: when this value is large, the response isquick to a change in steering, but when this value is small, theresponse is slow to a change in steering.

FIG. 9 is an explanatory diagram of the forces acted on the wheel. Theforces acted on the wheel include the cornering force described above, alongitudinal force Fx, a lateral force Fy, a vertical force Fz and soon. When turning by the wheel sliding angle βw, the component of thefrictional force along the direction parallel to the plane of the centerof the wheel is the longitudinal force Fx, the component of thefrictional force along the direction perpendicular to the plane of thecenter of the wheel is the lateral force Fy, and the vertical force Fzis the load in the vertical direction, called a vertical load.

Among the forces acted on the wheel listed above, the cornering forceand the lateral force Fy may be regarded as similar forces. While theseforces are not strictly identical, there is a tendency for these forcesto be approximately equal in the entire range of the wheel sliding angle13 w. In the present application, the cornering force and the lateralforce Fy are regarded as essentially the same. The relationship betweenthe lateral force Fy and the cornering power ka is described below.

The lateral force Fy can be expressed as in Eq. (37) in a quadratic formof the vehicle sliding angle βw, through the use of the tire model (aquadratic approximation model) of “Fiala” that can take into account theeffect of nonlinearities:

$\begin{matrix}{{Fy} = {{{k \cdot \beta}\; w} - {{\frac{k^{2}}{4{Fy}\mspace{11mu} \max} \cdot \beta}\; w^{2}}}} & (37)\end{matrix}$

In this case, the vehicle cornering power ka satisfies the relationshipexpressed as follows:

$\begin{matrix}{{ka} = {\frac{\partial{Fy}}{{\partial\beta}\; w} = {k - {\frac{k^{2}}{2\; {Fy}\mspace{11mu} \max} \cdot {{\beta \; w}}}}}} & (38)\end{matrix}$

That is, the cornering power ka is the rate of change (the differential)of the lateral force Fy with respect to an infinitesimal change in thevehicle sliding angle βw.

In Eqs. (37) and (38), the coefficient k is a constant that can beobtained experimentally, known as a reference cornering power. Thisreference cornering power k represents the characteristics of the wheel,and varies depending on the friction coefficient μ between the roadsurface and the wheel and also on the vertical force Fx. Specifically, alarge value of k indicates that the wheel has high stiffness, and asmall value of k indicates that the stiffness of the wheel is low. Thereference cornering power k is defined as the rate of change (thedifferential value) of the lateral force Fy at the point where the wheelsliding angle βw is 0, and is expressed as:

$\begin{matrix}{k = \left. \frac{\partial{Fy}}{{\partial\beta}\; w} \right|_{{\beta \; w} = 0}} & (39)\end{matrix}$

Further, a lateral force maximum value Fymax, which is the maximum valueof the lateral force Fy, is calculated uniquely based on the verticalforce Fz, the longitudinal force Fx, and the friction coefficient μ asshown in Eq. (40):

Fymax=√{square root over (μ² ·Fz ² −Fx ²)}  (40)

By considering the nonlinearities of the wheel, the elements a11-b2 canbe rewritten as in Eq. (41):

$\begin{matrix}{{{a\; 11} = {\frac{1}{M \cdot V}\left\{ {\underset{\underset{{Linear}\mspace{14mu} {Term}}{}}{2\left( {{kf} + {kr}} \right)} - \underset{\underset{{Nonlinear}\mspace{14mu} {Term}}{}}{\left( {{\frac{{kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}} + {\frac{{kr}^{2}}{{Fr\_ y}\mspace{11mu} \max} \cdot {{\beta \; r}}}} \right)}} \right\}}}{{a\; 12} = {1 + {\frac{1}{M \cdot V^{2}}\left\{ {\underset{\underset{{Linear}\mspace{14mu} {Term}}{}}{2\left( {{{lf} \cdot {kf}} - {{lr} \cdot {kr}}} \right)} - \underset{\underset{{Nonlinear}\mspace{14mu} {Term}}{}}{\left( {{\frac{{lf} \cdot {kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}} - {\frac{{lr} \cdot {kr}^{2}}{{Fr\_ y}\mspace{11mu} \max} \cdot {{\beta \; r}}}} \right)}} \right\}}}}{{a\; 21} = {\frac{1}{Iz}\left\{ {\underset{\underset{{Linear}\mspace{14mu} {Term}}{}}{2\left( {{{lf} \cdot {kf}} - {{lr} \cdot {kr}}} \right)} - \underset{\underset{{Nonlinear}\mspace{14mu} {Term}}{}}{\left( {{\frac{{lf} \cdot {kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}} - {\frac{{lr} \cdot {kr}^{2}}{{Fr\_ y}\mspace{11mu} \max} \cdot {{\beta \; r}}}} \right)}} \right\}}}{{a\; 22} = {\frac{1}{{Iz} \cdot V}\left\{ {\underset{\underset{{Linear}\mspace{14mu} {Term}}{}}{2\left( {{{lf}^{\mspace{11mu} 2} \cdot {kf}} + {{lr}^{2} \cdot {kr}}} \right)} - \underset{\underset{{Nonlinear}\mspace{14mu} {Term}}{}}{\left( {{\frac{{lf}^{\mspace{11mu} 2\;} \cdot {kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}} + {\frac{{lr}^{2} \cdot {kr}^{2}}{{Fr\_ y}\mspace{11mu} \max} \cdot {{\beta \; r}}}} \right)}} \right\}}}\mspace{20mu} {{b\; 1} = {\frac{1}{M \cdot V}\left\{ {{2\; {kf}} - {\frac{{kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}}} \right\}}}\mspace{20mu} {{b\; 2} = {\frac{lf}{Iz}\left\{ {{2{kf}} - {\frac{{kf}^{\mspace{11mu} 2}}{{Ff\_ y}\mspace{11mu} \max} \cdot {{\beta \; f}}}} \right\}}}} & (41)\end{matrix}$

In the above equations, kf is an equivalent cornering power of the frontwheel when the elastic deformation of the suspension is taken intoaccount for the front wheel reference cornering power, and kr is anequivalent cornering power of the rear wheel when the elasticdeformation of the suspension is taken into account for the rear wheelreference cornering power. In addition, βf is a front wheel slidingangle, and is the average value of the left and right front wheelsliding angles βw (termed “average front wheel sliding angle”), and βris the rear wheel sliding angle, and is the average value of the leftand right rear wheel sliding angles βw (termed “average rear wheelsliding angle”). These sliding angles βf and βr are expressed asfollows:

$\begin{matrix}{{{\beta \; f} = {{\beta \; b} + {\frac{l\; f}{V} \cdot \gamma} - {\delta \; f}}}{{\beta \; r} = {{\beta \; b} - {\frac{l\; r}{V} \cdot \gamma}}}} & (42)\end{matrix}$

The elements a11 and a22, which are diagonal elements in the systemmatrix, are parameters that have an impact on the stability of thevehicle (the degree of vehicle behavior convergence). In particular, theelement a11 autonomously stabilizes the lateral motion, and the elementa22 autonomously stabilizes the yawing behavior. Additionally, theelements a12 and a21, which are off-diagonal elements in the systemmatrix, are parameters that have an impact on improving the response ofthe vehicle (the degree of vehicle behavior variation). When theelements a12 and a21 are relatively small as compared to the elementsa11 and a22, the stability of the vehicle at high speed is improved. Incontrast, when the elements a12 and a21 are relatively large as comparedto the elements a11 and a22, the response of the vehicle to steering isimproved. The elements b1 and b2 are the gain of the vehicle behavior tosteering by the driver, and are adjustable via the steering gear ratio,for example.

In the present embodiment, an ideal vehicle is considered to be the onewith the vehicle behavior characteristics that are robust to changes inthe driving environment. Thus, of the elements a11-b2, the primary goalof control is to suppress changes in the elements a11-a22. When theelements a11-a22 are obtained analytically, each of the elements a11-a22is expressed as a sum of the terms that are dependent on the vehiclemass M, the various dimensions of the vehicle such as a wheel base, andthe equivalent cornering powers kf and kr, and of the terms that aredependent on the average front and rear sliding angles βf and βr, thevertical force Fz, and the friction coefficient μ, as shown in Equation41. In other words, each of the elements a11-a22 is expressed in termsof a linear term, which changes with the linear properties of the wheel,and the nonlinear term, which changes with the nonlinear properties ofthe wheel. When the elements a11-a22 change due only to the linearterms, the behavior of the wheels exhibits linear characteristics, andthus there are no particular problems from the perspective of stability.However, when the elements a11-a22 change due to the nonlinear terms aswell, the behavior of the wheels exhibits nonlinear characteristics,which may interfere with steering. Based on the knowledge that thechanges in the nonlinear terms are caused by the driving forcedistribution ratio between the front and rear wheels, the driving forcedistribution ratio between the front and rear wheels may be adjusted toreduce the absolute values of the nonlinear terms from the currentvalues (the absolute values of the current values) preferably to 0. Byminimizing the nonlinear terms in this way, the effects of the nonlinearterms in the elements a11-a22 are reduced, and the variations in theelements a11-a22 are suppressed.

In the following, the total driving force, which is the sum of thedriving forces applied to the wheels, is denoted by fa, and the drivingforce distribution ratio is denoted by r. Then, a front wheellongitudinal force Ff_x, which is the average of the longitudinal forcesFx for the left and right front wheels (termed “front wheel averagelongitudinal force”) and a rear wheel longitudinal force Fr_x, which isthe average of the longitudinal force Fx for the left and right rearwheels (termed “rear wheel average longitudinal force”) are expressed asfollows:

$\begin{matrix}{{{Fa} = {2\left( {{Ff\_ x} + {Fr\_ x}} \right)}}{{Ff\_ x} = {r \cdot \frac{Fa}{2}}}{{Fr\_ x} = {\left( {1 - r} \right) \cdot \frac{Fa}{2}}}} & (43)\end{matrix}$

Minimizing the Nonlinear Term in Element a11

FIG. 10 is an explanatory graph showing the trends of the driving forcedistribution ratio r that minimizes the nonlinear term in the elementa11. The nonlinear term in the element a11 is a linear combination ofthe absolute value of the average front wheel sliding angle βf and theabsolute value of the average rear wheel sliding angle βr. For the sakeof clarity, in the below the average rear wheel sliding angle βr isexpressed as s times the average front wheel sliding angle βf (wherethis factor s is called a “wheel sliding angle ratio”). FIG. 10illustrates the relationship between a body acceleration Acc (defined asthe total driving force Fa/vehicle mass M) and the driving forcedistribution ratio r for specific wheel sliding angle ratios (s=0.1,1.0, 10) under the condition of a constant friction coefficient (forexample, μ=0.9). (This condition is also true for FIGS. 12 and 13later.) As indicated in Eqs. (40), (41) and (42), the trends shown inthis figure can be obtained based on the friction coefficient μ, thetotal driving force Fa, an average value Ff_z of the vertical forces Fzon the left and right front wheels (termed “front wheel average verticalforce”), an average value Fr_z of the vertical forces Fz on the left andright rear wheels (termed “rear wheel average vertical force”) forindividual wheel sliding angle ratio s. For example, the values of thenonlinear term are calculated according to the different driving forcedistribution ratios r, and the driving force distribution ratio r thatgives the smallest absolute value of the nonlinear term may be selected.If the wheel sliding angle ratio s is 1.0, the driving forcedistribution ratio r is in a range between about 0.5 and 0.8, with moreweight on the front wheels. If the wheel sliding angle ratio s is lessthan 1.0, there is a tendency towards having more weight on the rearwheels. If the wheel sliding angle ratio s is greater than 1.0, there isa tendency towards having more weight on the front wheels than the caseof the wheel sliding angle ratio s equal 1.0.

Minimizing the Nonlinear Terms in the Elements a12 and a21

FIG. 11 is an explanatory graph showing the trends of the driving forcedistribution ratio r that minimizes the nonlinear terms in the elementsa12 and a21. Each of the nonlinear terms in the elements a12 and a21 isa linear combination of the absolute value of the average front wheelsliding angle βf and the absolute value of the average rear wheelsliding angle βr, and both are expressed by identical polynomials. Thetrends shown in FIG. 11 are obtained uniquely based on the parametersdescribed above, in the same manner as for the element a11.Specifically, if the wheel sliding angle ratio s is 1.0, the drivingforce distribution ratio r is greater than about 0.7, showing an evengreater tendency of having weight on the front wheels than in the caseof the element a11. On the other hand, if the wheel sliding angle ratios is less than 1.0, the tendency is for the weight to be more on therear wheels than in the case of the wheel sliding angle ratio s equal1.0. If the wheel sliding angle ratio s is greater than 1.0, there is nosolution between 0.0 and 1.0.

Minimizing the Nonlinear Term of Element a22

FIG. 12 is an explanatory graph showing the trends of the driving forcedistribution ratio r that minimizes the nonlinear term in the elementa22. The nonlinear term in the element a22 is a linear combination ofthe absolute value of the average front wheel sliding angle βf and theabsolute value of the average rear wheel sliding angle βr. The trendsshown in FIG. 12 are obtained uniquely in the same manner as for theelements a11-a12, based on the friction coefficient μ, the total drivingforce Fa, and the front and rear average vertical forces Ff_z and Fr_z.Specifically, overall, there is a greater tendency of having weight onthe front wheels than in the case of the element a11.

Any one of the elements a11 to a22 may be selected for minimizing thenonlinear term. Note that the average front wheel sliding angle βf andthe average rear wheel sliding angle βr, included in the nonlinearterms, are difficult to measure precisely in actual measurements; thus,it is difficult to reflect these values βf and βr in the control system.Therefore, in the range where the wheel sliding angle βw is small, thefront and rear wheel lateral forces Ff_y and Fr_y, which are detectable,are substituted, respectively, for the average front wheel sliding angleβf and average rear wheel sliding angle βr, based on the observationthat the arithmetic product of the reference cornering power (theequivalent cornering power) k and the wheel sliding angle βw correspondsto the lateral force Fy. In other words, the nonlinear term in each ofthe elements a11 to a22 is expressed based on the set of parametersdescribed above, those parameters being μ, Fa, Ff_z and Fr_s along withan average value of the left and right front wheel lateral forces Fy(termed “front wheel average lateral force” Ff_y), and an average valueof the left and right rear wheel lateral forces Fy (termed “rear wheelaverage lateral force” Fr_y). The resultant nonlinear term of theelement a11 is given in Eq. (44):

$\begin{matrix}{{{kf} \cdot \frac{{Ff\_ y}}{\sqrt{{\mu^{2} \cdot {Ff\_ z}^{2}} - {r^{2} \cdot \frac{{Fa}^{2}}{4}}}}} + {{kr} \cdot \frac{{Fr\_ y}}{\sqrt{{\mu^{2} \cdot {Fr\_ z}^{2}} - {\left( {1 - r} \right)^{2} \cdot \frac{{Fa}^{2}}{4}}}}}} & (44)\end{matrix}$

Similar substitutions can be made for the nonlinear terms of the otherelements a12-a22. The detailed explanations are omitted here because thefundamental concepts are the same, except to note that the driving forcedistribution ratios r that minimizes the nonlinear term in each of theelements a12-a22 can be obtained also based on the friction coefficientμ, the front and rear wheel average vertical forces Ff_z and Fr_z, thefront and rear wheel average lateral forces Ff_y and Fr_y and the totaldriving force Fa.

The system configuration of the vehicle motion control device accordingto the present embodiment is explained below based on the conceptualexplanation given above. FIG. 13 is an explanatory diagram of a vehicleto which the vehicle motion control device 71 according to the presentembodiment is applied. This vehicle is a four-wheel drive vehicle,driven by both the front and rear wheels. The driving force from a crankshaft (not shown) of an engine 72 is transmitted through an automatictransmission 73 and a center differential device 74 to front wheel andrear wheel drive axles 75. When the driving force is transmitted to thedrive axles 75, rotational torques are applied to the front wheels 76 fand the rear wheels 76 r, causing the front wheels 76 f and rear wheels76 r to rotate, thereby producing the driving forces for the front andrear wheels 76 f and 76 r. Note that in the present embodiment a simpleterm “wheels 76” is used to indicate the front wheels 76 f and the rearwheels 76 r.

The center differential device 74 is a compound planetary gear-typedifferential control device. Between the two output sections of thecenter differential device 74, that is, between the front wheel-sideoutput section (a carrier 74 a) and the rear wheel-side output section(a sun gear 74 b), a hydraulic multi-board clutch 74 c is provided. Inthis hydraulic multi-board clutch 74 c, the automatic engagement statuscan be adjusted through adjusting the hydraulic pressure using asolenoid valve 74 d (i.e., through increasing, maintaining, ordecreasing the hydraulic pressure). When the hydraulic multi-boardclutch 74 c is disengaged, the differential movement of the front andrear drive axles 75 occurs, and thus the driving force distributionratio r depends on the value predetermined by the center differentialdevice 74 (for example, r=0.35). On the other hand, when the hydraulicmulti-board clutch 74 c is fully engaged, the differential movement ofthe front and rear drive axles 75 is suppressed, giving rise to thedriving force distribution ratio r corresponding to the state where thefront and rear drive axles 75 are rigidly connected. In other words, thedriving force distribution ratio r is varied by the state of engagementof the hydraulic multi-board clutch 74 c.

FIG. 14 is a block diagram showing the overall structure of the vehiclemotion control device 71. The vehicle motion control device 71 comprisesa control unit 80, which may be a microcomputer comprising a CPU, a ROM,a RAM, and an I/O interface. The control unit 80 performs calculationspertaining to the vehicle motion control through a control programstored in the ROM. Functionally, the microcomputer as the control unit80 comprises a calculating unit 80 a and a setting unit 80 b. In thepresent embodiment, the calculating unit 80 a obtains the nonlinearterms of the elements of the system matrix (a11 is chosen in the presentembodiment). The setting unit 80 b obtains a target driving forcedistribution ratio r′ with the above nonlinear terms obtained. In orderto perform these calculations, the control unit 80 receives not onlydetection signals from a variety of sensors, including a detecting unit81, but also a variety of values (the friction coefficient μ and thetotal driving force Fa in the present embodiment) estimated by anestimating unit 82 (not shown in FIG. 13).

The detecting unit 81 comprises sensors for detecting forces applied tothe wheels 76. In FIG. 14, only a single block is shown for thedetecting unit 81 for convenience, but actually the detecting unit 81 isprovided for each of the four wheels 76. Each of the detecting units 81can individually detect the longitudinal force Fx, the lateral force Fyand the vertical force Fz. The detecting unit 81 comprises a straingauge and a signal processing circuit that generates detection signalsaccording to the applied force through processing the electrical signalsoutputted from the strain gauge. The strain that occurs in the driveaxles 75 is proportional to the applied force, and the detecting unit 81directly detects the applied force via the strain gauges embedded in theaxles 75. Note that specific structures of the detecting unit 81 aredescribed in, for example, Japanese Kokai Laid-open Publication H04-331336 and Japanese Kokai Laid-open Publication H 10-318862. Theentire disclosures of Japanese Kokai Laid-open Publications H 04-331336and 1-10-318862 are incorporated herein by reference. The estimatingunit 82, as described below, estimates the friction coefficient μ a andthe total driving force Fa based on the detection results from a varietyof sensors, not shown.

FIG. 15 is a flowchart showing the vehicle control sequence according tothe present embodiment. The procedure shown in this flowchart is calledat specific intervals, and is executed by the vehicle motion controldevice 71. First, in Step 1, the various detection signals are read in.The detection values that are read in at this Step 1 include the forcesapplied to each of the wheels 76 (the lateral force Fy and the verticalforce Fz).

The friction coefficient μ and the total driving force Fa are estimatedin Step 2. One well-known method for estimating the friction coefficientis, for example, based on the vehicle motion model wherein the behaviorof the vehicle is modeled based on the vehicle motion theory. In thismethod, the actual state of motion of the vehicle (for example, thesliding angle) is used as the basis for estimating the current frictioncoefficient μ, by comparing between the state of motion in the vehiclemotion model that assumes a high μ road and the state of motion in thevehicle motion model that assumes a low μ road. The details of this typeof method for estimating the friction coefficient μ are disclosed in,for example, Japanese Kokai Laid-open Publication 200-071968. Inaddition, the friction coefficient μ may be estimated based on theacceleration and the difference in velocity between two of the wheels76, as disclosed in, for example, Japanese Kokai Laid-open Publication2003-237558. Moreover, as disclosed in Japanese Kokai Laid-openPublication 2002-27882, the friction coefficient μ may be estimated byincorporating the conditions of the road surface, detected by a camera,in the state of motion of the vehicle. As seen above, a wide variety ofmethods may be used to estimate the friction coefficient μ, based on thestate of the vehicle, in the present embodiment. Here, the state of thevehicle is represented by the sliding angle, the yaw rate, the wheelvelocity, the state of the road surface contacted by the wheels 76, andthe like. The entire disclosures of Japanese Kokai Laid-openPublications 200-071968, 2003-237558, and 2002-27882 are incorporatedherein by reference.

The total driving force Fa is obtained based on the torque outputtedfrom the engine 72 according to the engine rotation number, and on thetorque outputted from the automatic transmission 73 according to theshift position and the like. Specifically, the velocity ratio of thetorque converter is calculated based on the engine rotation number andthe turbine rotation number of the torque converter in the automatictransmission 73. Based on the results, a map showing the relationshipbetween the velocity ratio of the torque converter and a pump capacitycoefficient is referenced to determine the pump capacity coefficientcorresponding to the calculated velocity ratio. Moreover, a torqueratio, which is defined as the ratio between the torque on the inputside of the torque converter and the torque on the output side of thetorque converter, corresponding to the calculated velocity ratio of thetorque converter is determined with reference to a map showing therelationship between the velocity ratio of the torque converter and thetorque ratio.

Thereafter, a pump torque is calculated based on the pump capacitycoefficient that has been determined and on the engine rotation number.Then, a turbine torque, outputted from the turbine, is calculated basedon the pump torque and the torque ratio. Moreover, an output torque ofthe automatic transmission 73 is calculated by multiplying the turbinetorque by the gear ratio corresponding to the current gear position.Finally, a driving torque is calculated by multiplying the output torqueof the automatic transmission 73 by the final gear ratio of theautomatic transmission 73. Thus the total driving force Fa is calculatedbased on the radius of the wheels and the driving torque.

The driving force distribution ratio target value r* is calculated inStep 3. The driving force distribution ratio r that minimizes thenonlinear term in element a11 can be obtained using Eq. (44).Specifically, the driving force distribution ratio r is varied in astepwise manner between 0.00 and 1.00, and the values of the nonlinearterm are sequentially calculated using the friction coefficient μ, thetotal driving force Fa, the average vertical forces Ff_z and Fr_z of thefront and rear wheels 76 f and 76 r, and the average lateral forces Ff_yand Fr_y of the front and rear wheels 76 f and 76 r. The driving forcedistribution ratio r that yields the smallest of the calculatednonlinear term values is set as the target value r*. Note that theaverage lateral forces Ff_y and Fr_y for the front and rear wheels 76 fand 76 r and the average vertical forces Ff_z and Fr_z for the front andrear wheels 76 f and 76 r can be determined uniquely based on therespective detected values (of the lateral force Fy and the verticalforce Fz) for each of the wheels 76.

In Step 4, the current value rc of the driving force distribution ratior is compared to the target value r* to determine whether or not thedifference between these values is greater than a threshold value rth.This threshold value rth is predetermined, through experiments andsimulations, to be the maximum value of the difference between aspecific current value rc and the target value r*, the specific currentvalue rc being the value at which control is regarded as not necessaryfrom the perspective of suppressing hunting in control. If the answer isyes in Step 4, or in other words, if the difference between the twovalues is greater than the threshold value (|rc−r*|>rth), the routineproceeds to Step 5. On the other hand, if the answer is no in Step 4, orin other words, if the difference between the values is less than thethreshold value rth (|rc−r*|<rth), the routine is exited withoutperforming Step 5.

In Step 5, a map that describes the relationship between the drivingforce distribution ratio r and the state of engagement (the engagementtorque) is referenced to output a control signal Sigr (a value thatindicates the engagement torque), corresponding to the predeterminedtarget value r*, to the solenoid valve 74 d; thereafter, the routine isexited. In this way, the state of engagement of the hydraulicmulti-board clutch 74 c is adjusted through controlling the duty ratioof the solenoid valve 74 d according to the control signal Sigr. Thischanges the driving force distribution ratio r from the current value rcto the target value r*.

In the present embodiment, the target value r* is determined to be thedriving force distribution ratio r that minimizes the absolute value ofthe nonlinear term of the element a11 in the system matrix. Moreover,the center differential device 74 (more specifically, the solenoid valve74 b) is controlled to vary the driving force distribution ratio rbetween the front wheels 76 f and rear wheels 76 r based on the targetvalue r*. Thus, the nonlinear term in the element a11 is minimized tocontrol the nonlinear components that act on the wheels 76, therebyleading to stabilized vehicle response. Moreover, minimizing thenonlinear term suppresses the variations in the element a11, which has astrong correlation to the convergence of the vehicle body sliding angle,thereby realizing stabilized vehicle response regardless of the drivingconditions.

Furthermore, the detecting unit 81 detects directly the applied forcesthat act on the wheels 76. Therefore, even in the “limit cornering”driving condition or while driving on a road with a low frictioncoefficient, the applied forces can be determined accurately. Therefore,the accuracy is improved in the calculations of the nonlinear term ofthe element a11, and more effective control of the state of motion ofthe vehicle is achieved.

Note that in the present embodiment, the driving force distributionratio r that minimizes the nonlinear term was uniquely determined to bethe target value r*. However, from the perspective of stability incontrol, it is adequate to set the target value r* so as to make theabsolute value of the nonlinear term only smaller than the currentabsolute value. For example, the current driving force distributionratio r may be changed by only a step value. Even in this method, thenonlinear components that act on the wheels 76 will be more controlledthan in the current situation, making it possible to obtain stabilizedvehicle response. This type of alternate method regarding theminimization of nonlinear terms can be employed similarly in the otherembodiments described later.

In the present embodiment, from the perspective that measuring theaverage front wheel sliding angle βf and the average rear wheel slidingangle 13 r is difficult, the average lateral forces Ff_y and Fr_y of thefront and rear wheels are substituted in obtaining the driving forcedistribution ratio r. However, as can be seen from the nonlinear termsin Eq. (41), the nonlinear terms may be calculated using the set ofparameters comprising μ, Fa, Ff_z, and Fr_z and the average front andrear sliding angles βf and βr. In this case, the average front and rearsliding angles βf and βr may be determined uniquely based on Eq. (42) bydetecting the vehicle body sliding angular velocity βb′ and integratingit in the estimating unit 82.

Third Embodiment

In the second embodiment, the values of the nonlinear term werecalculated while varying the driving force distribution ratio r from0.00 to 1.00 in a stepwise manner in Eq. (44) to thereby determine thetarget value r* which is the driving force distribution ratio r thatyields the smallest of the calculated nonlinear term values. However, inEq. (44) there are some cases wherein the value in the square rootbecomes negative, so that it is not possible to obtain the driving forcedistribution ratio r. Therefore, in actual control, it is preferable todetermine the driving force distribution ratio r using the followingexpression:

$\begin{matrix}{{{kf} \cdot \frac{{Ff\_ y}}{\sqrt{{\mu^{2} \cdot {Ff\_ z}^{2}} - \left( {{Ff\_ Lim} - {\frac{r}{2} \cdot {Ff\_ div}}} \right)^{2}}}} + {{kr} \cdot \frac{{Fr\_ y}}{\sqrt{{\mu^{2} \cdot {Fr\_ z}^{2}} - \left( {{Ff\_ Lim} - {\frac{1 - r}{2} \cdot {Fr\_ div}}} \right)^{2}}}}} & (45)\end{matrix}$

where Ff_Lim is a per-wheel maximum value of the driving force appliedto the front wheels 76 f (hereinafter termed “front wheel maximumvalue”), which is the product of the friction coefficient μ and theper-wheel vertical force Ff_z for the front wheels 76 f; and Fr_Lim is aper-wheel maximum value of the driving force applied to the rear wheels76 r (hereinafter termed “rear wheel maximum value”), which is theproduct of the friction coefficient μ and the per-wheel vertical forceFr_z for the rear wheels 76 r. Ff_div and Fr_div are expressed in therelationships as follows:

$\begin{matrix}{{{Ff\_ div} = {{\sum{Ff\_ Lim}} - \frac{Fa}{2}}}{{Fr\_ div} = {{\sum{Fr\_ Lim}} - \frac{Fa}{2}}}} & (46)\end{matrix}$

Note that since Ff_Lim and Fr_Lim are quantities separately obtained forthe left and right wheels, the summation sign Σ shown in Eq. (46)indicates the sum over the two front wheels or the sum over the two rearwheels. Using the relationships in Eq. (46) is one of the methods tocalculate the driving force distribution ratio r based on Eq. (45).

Although only the nonlinear term of the element a11 is shown above,similar substitutions can be made for the nonlinear terms in the otherelements a11-a22 as well. Although the explanations are omitted becausethe fundamental concept is the same, the nonlinear terms in the elementsa11-a22 are calculated using the front wheel maximum value Ff_Lim, therear wheel maximum value Fr_Lim, the front and rear wheel averagelateral forces Ff_y and Fr_y, and the parameters μ, Fa, Ff_z, and Fr_z.The use of the present method can improve reliability in control sincethe situation wherein there is no solution for the driving forcedistribution ratio r can be avoided, and the similar effects as in thesecond embodiment can be achieved.

Fourth Embodiment

In the third embodiment, expansion is carried out in Eq. (44) throughinputting the front and rear wheel average lateral forces Ff_y and Fr_ycaused by steering. Even for driving in a straight line, when additionalforces (especially to the average lateral forces Fy) are applied asexternal noises due to unevenness of the road surfaces, crosswinds, andthe like, it is possible to minimize the nonlinear terms in the elementsof a11-a22 using the concept described above. However, unlike the caseof steering, when driving in a straight line it is difficult to estimatethe average lateral forces Ff_y and Fr_y of the front and rear wheels,and thus it is assumed that the average lateral forces Ff_y and Fr_y ofthe front and rear wheels are identical. In this case, the nonlinearterm of the element a11 can be expressed as follows:

$\begin{matrix}{\frac{kf}{\sqrt{{\mu^{2} \cdot {Ff\_ z}^{2}} - \left( {{Ff\_ Lim} - {\frac{r^{\prime}}{2} \cdot {Ff\_ div}}} \right)^{2}}} + \frac{kr}{\sqrt{{\mu^{2} \cdot {Fr\_ z}^{2}} - \left( {{Ff\_ Lim} - {\frac{1 - r^{\prime}}{2} \cdot {Fr\_ div}}} \right)^{2}}}} & (47)\end{matrix}$

Although only the nonlinear term of the element a11 is shown above,similar substitutions can be made for the nonlinear terms in the otherelements a12-a22 as well. Although the explanations are omitted becausethe fundamental concept is the same, the nonlinear terms in the elementsa11-a22 are calculated using the front wheel maximum value Ff_Lim, therear wheel maximum value Fr_Lim, and the parameters μ, Fa, Ff_z, andFr_z.

Fifth Embodiment

FIG. 16 is an explanatory diagram showing the state surface. Theanalytical method by use of the “state surface” is effective fornonlinear control systems wherein the control inputs change discretely,as in the state of motion for a vehicle that is affected by thenonlinear characteristics of the wheels, for example. For a vehiclewherein the state of motion is expressed in terms of the equation ofstate based on a two-wheel model, the state surface is expressed interms of a vector field S (β′(βb, γ), γ′ (βb, γ)), which has the axesrepresenting the vehicle body sliding angle βb and the yaw rate γ. Inthe vector field S, the more the vectors point outwardly, the moredivergent the state surface (the vehicle behavior) is; and the more thevectors point inwardly, the more non-divergent the state surface (thevehicle behavior) is. When the state surface has non-divergenttendencies, the divergence of the vehicle behavior is suppressed evenwhen there are disturbances, thereby leading to stabilized vehicleresponse.

The tendency of the vectors in the vector field may be evaluatedquantitatively using a characteristic value known as divergence ∇S. Thedivergence ∇S is the sum of the partial differential of the vehicle bodysliding angular velocity βb′ with respect to the vehicle body slidingangle βb, and the partial differential of the yaw angular accelerationγ′ with respect to the yaw rate γ. When the divergence ∇S is positive,the vectors have a tendency to point outwardly; and when this divergence∇S is negative, the vectors have a tendency to point inwardly.Consequently, minimizing the divergence ∇S in the vector field S causesthe vectors to point inwardly, thereby suppressing the divergence of thevehicle behavior.

In the present embodiment, based on the concept described above, thedriving force distribution ratio r is controlled so as to minimize thedivergence ∇S in the vector field S that represents the state surface.Note that in the present embodiment, the term “minimize the divergence∇S” is used to mean not only to cause the value ∇S to have the smallestvalue in the possible range, but also to cause this value ∇S to have avalue that is merely smaller than the current value. Calculating thedivergence □S using the equations of state in Eqs. (35) and (36) leadsto the following expression:

$\begin{matrix}\begin{matrix}{{\bigtriangledown \; S} = {\frac{{\partial\beta}\; b^{\prime}}{{\partial\beta}\; b} + \frac{\partial\gamma^{\prime}}{\partial\gamma}}} \\{= {- {2\begin{bmatrix}{\underset{{Linear}\mspace{14mu} {Term}}{\underset{}{\left( {\frac{{kf} + {kr}}{M \cdot V} + \frac{{{lf}^{\; 2} \cdot {kf}} + {{lr}^{2} \cdot {kr}}}{{Iz} \cdot V}} \right)}} -} \\\underset{{Nonlinear}\mspace{14mu} {Term}}{\underset{}{\begin{Bmatrix}{{\left( {\frac{{kf}^{\; 2}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\; 2}}{{Iz} \cdot V}} \right){\left( \frac{1}{{Ff\_ y}\; \max} \right) \cdot {{\beta \; f}}}} +} \\{\left( {\frac{{kr}^{2}}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}^{2}}{{Iz} \cdot V}} \right){\left( \frac{1}{{Fr\_ y}\; \max} \right) \cdot {{\beta \; r}}}}\end{Bmatrix}}}\end{bmatrix}}}} \\{= {{{- \frac{2}{M \cdot V}} \cdot \left( {{kf\_ a} + {Kr\_ a}} \right)} - {\frac{2}{{Iz} \cdot V}\left( {{{lf}^{\; 2} \cdot {kf\_ a}} + {{lr}^{2} \cdot {kr\_ a}}} \right)}}} \\{= \left( {{a\; 11} + {a\; 22}} \right)}\end{matrix} & (48)\end{matrix}$

As shown in Eq. (48), the divergence □S of the vector field S isexpressed as the sum of a linear term and a nonlinear term, as was thecase in the first embodiment. Moreover, the divergence □S is equivalentto the negative of the sum of the diagonal elements of a11 and a22 inthe system matrix. Because the linear term in the sum of the diagonalelements a11 and a12 is always positive, in order to minimize thedivergence □S, the absolute value of the nonlinear term, which has aminus sign, should be minimized (that is, minimizing the nonlinearterm).

The driving force distribution ratio r can be expressed as below bysubstituting Eq. (43) into the nonlinear term in Eq. (48):

$\begin{matrix}{{\left( {\frac{{kf}^{\; 2}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\; 2}}{{Iz} \cdot V}} \right){\left( \frac{1}{\sqrt{{\mu^{2} \cdot {Ff\_ z}^{2}} - {r^{2} \cdot \frac{{Fa}^{2}}{4}}}} \right) \cdot {{\beta \; f}}}} + {\left( {\frac{{kr}^{2}}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}^{2}}{{Iz} \cdot V}} \right){\left( \frac{1}{\sqrt{{\mu^{2} \cdot {Ff\_ z}^{2}} - {\left( {1 - r} \right)^{2} \cdot \frac{{Fa}^{2}}{4}}}} \right) \cdot {{\beta \; r}}}}} & (49)\end{matrix}$

Specifically, values of the nonlinear term are calculated sequentiallyusing the friction coefficient μ, the total driving force Fa, the frontand rear wheel average vertical forces Ff_z and Fr_z, and the front andrear wheel average sliding angles βf and βr while varying the drivingforce distribution ratio r from 0.00 to 1.00 in a stepwise manner. Thedriving force distribution ratio r that yields the smallest of thecalculated nonlinear term values is set as the target value r*. Notethat when performing calculations sequentially in this way, it isdifficult to measure accurately the values of the front and rear wheelaverage sliding angles βf and βr. Therefore, the sliding angles βf andβr may be replaced, respectively, with the front and rear wheel averagelateral forces Ff_y and Fr_y, which are detectable, as was explained inthe first embodiment.

In the present embodiment, the target value r* of the driving forcedistribution ratio r is determined so as to minimize the divergence □Sof the vector field S that represents the state surface. Therefore,steering is improved, through controlling the vehicle responses (such asspinning, etc.) resulting from the nonlinear properties of the wheels.

In the present embodiment, the nonlinear term in the divergence □S iscalculated, and the driving force distribution ratio r is determined soas to reduce the nonlinear term to be smaller than the current value.Note that minimizing the nonlinear term is equivalent to minimizing thedivergence □S. Therefore, the series of control steps described abovemay be restated as the procedure described as follows: in the firststep, the divergence □S is calculated in the calculating unit 80 a; andin the second step, the driving force distribution ratio r that makesthe divergence □S less than the current value is set in the setting unit80 b. Note that when the divergence □S is less than or equal to zero,the state surface has non-divergent tendencies; thus, it is possible toset as the target value r* a driving force distribution ratio value rthat makes the divergence □S less than or equal to zero, rather thansetting as the target value r* the driving force distribution ratiovalue r that minimizes the divergence □S. In other words, when there isa constraint that the current value □S be negative, a driving forcedistribution ratio value r that makes the divergence □S large may beselected as the target value r*.

In the individual embodiments so far, the vehicle body sliding angle βband the yaw rate γ are used as the axes in the vector field forexpressing the state surface, because of the use of the equations ofstate based on the two-wheel model. However, any parameters may be usedas the axes, as long as they are state variables that express the stateof motion of the vehicle, such as the lateral force Fz and the yawmoment, or the vehicle body sliding angle βb and the vehicle bodysliding angular velocity βb′.

Sixth Embodiment

A vehicle wherein the state of motion is described with the equations ofstate based on a two-wheel model may be considered to be equivalent toan oscillator system with one degree of freedom, which is a time lagsystem of the second order. This oscillator system can be modeled as afree oscillator including damping, wherein the properties are expressedthrough two state variables, i.e. an angular eigen frequency ωn, and adamping ratio ζ. In the equations of state for the oscillator systemwith one degree of freedom, the angular eigen frequency ωn and the dutyratio ζ are expressed by the formulas below:

$\begin{matrix}{{{\omega \; n} = {\sqrt{{{- \frac{c}{m}} \cdot 0} - \left( {{- \frac{k}{m}} \cdot 1} \right)} = \sqrt{\frac{k}{m}}}}{\zeta = {{\frac{c}{2 \cdot m} \cdot \frac{1}{\sqrt{\frac{k}{m}}}} = \frac{c}{2\sqrt{m \cdot k}}}}{{\omega \; {n \cdot \zeta}} = {{{- \frac{1}{2}} \cdot \left( {{- \frac{c}{m}} + 0} \right)} = \frac{c}{2m}}}} & (50)\end{matrix}$

where m is a mass, c is a damping factor, and k is a spring constant.The angular eigen frequency ωn is the square root of the spring constantk divided by the mass m, and the damping ratio ζ is the damping factor cdivided by twice the square root of the product of the mass m and thespring constant k.

The product of the angular eigen frequency ωn and the damping ratio ζ isa characteristic value representing the convergence of the oscillatorsystem; thus, this product is mainly focused in the present embodiment(this product simply termed “damping” below). By taking into account theequivalence between the oscillator system and the motion of a vehicle (avehicle system), and using the equations of state describing the stateof motion of a vehicle (Eq. (35)), ωn, ζ, and ωn·ζ can be expressed asfollows:

$\begin{matrix}{{{\omega \; n} = \sqrt{{a\; {11 \cdot a}\; 22} - {a\; {12 \cdot a}\; 21}}}{\zeta = \frac{{a\; 11} + {a\; 22}}{2 \cdot \sqrt{{a\; {11 \cdot a}\; 22} - {a\; {12 \cdot a}\; 21}}}}{{\omega \; {n \cdot \zeta}} = \frac{{a\; 11} + {a\; 22}}{2}}} & (51)\end{matrix}$

As seen above, the angular eigen frequency ωn of the vehicle system isthe square root of the difference between the product of the diagonalelements a11 and a22 and the product of the off-diagonal elements a12and a21 in the system matrix, the damping factor ζ of the vehicle systemis the sum of the diagonal elements a11 and a22 divided by a value thatis twice the angular eigen frequency ωn, and the damping ωn·ζ of thevehicle system is a value that is one half of the sum of the diagonalelements a11 and a22, or in other words, equal to the average of thediagonal elements a11 and a22. The larger the damping ωn·ζ is, thegreater the convergence of the oscillator system to disturbances is. Inother words, the larger the damping ωn·ζ is, the greater the stabilityof the vehicle is.

In the present embodiment, the driving force distribution ratio r iscontrolled so as to maximize the damping ωn·ζ based on the aboveconcept. Note that in the present embodiment, the phrase “maximize thedamping ωn·ζ” is used to mean not only to cause the value of ωn·ζ tohave the maximum value in the possible range, but also to cause thevalue of ωn·ζ to be merely larger than the current value (that is, tosuppress any reductions in the damping ωn·ζ). Because the linear term inthe sum of the diagonal elements a11 and a22 is always positive, inorder to maximize the damping ωn·ζ, the absolute value of the nonlinearterm, which has a minus sign, should be minimized (that is, minimizingthe nonlinear term). The driving force distribution ratio r thatminimizes the nonlinear term can be determined based on Eq. (49) as inthe same manner as minimizing the divergence □S.

According to the present embodiment, the driving force distributionratio r is determined so as to maximize the damping ωn·ζ to improve theconvergence of the system, from the perspective of the equivalencebetween the state of motion of the vehicle and the oscillator systemwith one degree of freedom, which is a time lag system of the secondorder. Therefore, the stability and steering of the vehicle areimproved.

Note that in the present embodiment, the driving force distributionratio r was determined so as to make the nonlinear term less than thecurrent value, and that minimizing the nonlinear term can be viewed asbeing equivalent to maximizing the damping ωn·ζ. Therefore, the seriesof control steps described above may be restated as the proceduredescribed as follows: in the first step, the damping ωn·ζ is calculatedin the calculating unit 80 a; and in the second step, the driving forcedistribution ratio r that makes the damping ωn·ζ less than the currentvalue is set in the setting unit 80 b.

Seventh Embodiment

Although in the second-seventh embodiments, a nonlinear term of one ofthe elements a11-a22 was minimized, nonlinear terms of two or more ofthe elements a11-a22 may be minimized. For example, the nonlinear termsof the sum of the elements a11 and a22 (the diagonal elements) may beminimized. The minimization of the nonlinear terms in the sum of theelements a11 and a22 can be done through the appropriate selection ofthe driving force distinction ratio r using Eq. (49). Such effects asshown, for example, in the fifth and sixth embodiments can be achievedby using a plurality of elements a11-a22, rather than only one of theelements a11-a22.

Eighth Embodiment

In the second-seventh embodiments, methods were presented whereby thedriving force distribution ratio r for the front and rear wheels wascontrolled. The present invention is not limited thereto, but rather thedriving force distribution ratio may be controlled for individual wheels(four wheels in the present embodiment) including the left and rightwheels. The present eighth embodiment presents a case wherein thedriving force distribution control is made for the individual wheelsbased on the control concept according to the fifth embodiment. Detailedexplanations are omitted, however, since the basic concept is the same.For the sake of explanations, the notations showing the state variablesare differentiated for individual wheels by using the letters “fl” toindicate the front left wheel, “fr” to indicate the front right wheel,“rl” to indicate the rear left wheel, and “rr” to indicate the rearright wheel. For example, kfl_a and kfr_a denote the cornering powers kafor the left and right front wheels, respectively, and krl_a and krr_aindicate the cornering powers ka for the left and right rear wheels,respectively (with the same convention holding for the other statevariables as well).

The cornering power kf_a for the front wheels is the average of thecornering powers kfl_a and kfr_a for the left and right front wheels,and the cornering power kr_a for the rear wheels is the average of thecornering powers krl_a and krr_a for the left and right rear wheels. Thecornering powers kfl_a through krr_a for the respective wheels can becalculated using Eq. (37), which is the equation for the per-wheelcornering power ka. By taking into account the four wheels individuallyin Eq. (38), the divergence □S is expressed as follows:

$\begin{matrix}{{\bigtriangledown \; S} = {- {2\begin{bmatrix}{\underset{{Linear}\mspace{14mu} {Term}}{\underset{}{\left( {\frac{{kf} + {kr}}{M \cdot V} + \frac{{{lf}^{\; 2} \cdot {kf}} + {{lr}^{2} \cdot {kr}}}{{Iz} \cdot V}} \right)}} -} \\\underset{{Nonlinear}\mspace{14mu} {Term}}{\underset{}{\begin{Bmatrix}{{\left( {\frac{{kf}^{\; 2}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\; 2}}{{Iz} \cdot V}} \right){\left( {\frac{1}{2{Ffl\_ y}\; \max} + \frac{1}{2{Ffr\_ y}\; \max}} \right) \cdot {{\beta \; f}}}} +} \\{\left( {\frac{{kr}^{2}}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}^{2}}{{Iz} \cdot V}} \right){\left( {\frac{1}{2{Frl\_ y}\; \max} + \frac{1}{2{Frr\_ y}\; \max}} \right) \cdot {{\beta \; r}}}}\end{Bmatrix}}}\end{bmatrix}}}} & (52)\end{matrix}$

where Ffl_ymax−Frr_ymax are the lateral force maximum values Fymax forthe respective four wheels.

Here the driving force distribution ratio between the front and rearwheels (hereinafter termed “front/rear distribution ratio”) is denotedby Rfr, the driving force distribution ratio between the left and rightwheels in the front (hereinafter termed “front left/right distributionratio”) is denoted by Rlr_f, and the driving force distribution ratiobetween the left and right wheels in the rear (hereinafter termed “rearleft/right distribution ratio”) is denoted by Rlr_r. The longitudinalforces Ffl_x−Frr_x can be expressed in terms of the driving forcedistribution ratios Rfr−Rlr_r and the total driving force Fa as follows:

Ffl _(—) x=Rfr·Rlr _(—) f·Fa

Ffr _(—) x=Rfr·(1−Rlr _(—) f)·Fa

Frl _(—) x=(1−Rfr)·Rlr _(—) r·Fa

Frr _(—) x=(1−Rfr)·(1−Rlr _(—) r)·Fa  (53)

In order to minimize the divergence □S, the absolute value of thenonlinear term, which has a minus sign, should be minimized (that is,minimizing the nonlinear term), In Eq. (52), the individual lateralforce maximum values Ffl_ymax−Frr_ymax can be obtained using Eq. (40),which is the equation for calculating the per-wheel lateral forcemaximum value Fymax. Reorganizing the nonlinear term in Eq. (52) by useof Eq. (53), the nonlinear term that should be minimized with respect tothe distribution ratios Rfr, Rlr_f and Rlr_r is expressed as follows:

$\begin{matrix}{{\left( {\frac{{kf}^{\; 2}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\; 2}}{{Iz} \cdot V}} \right)\left( {\frac{1}{\sqrt{{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {{Rfr}^{2} \cdot {Rlr\_ f}^{2} \cdot {Fa}^{2}}}} + \frac{1}{\sqrt{{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {{Rfr}^{2} \cdot \left( {1 - {Rlr\_ f}} \right)^{2} \cdot {Fa}^{2}}}}} \right){{\beta \; f}}} + {\left( {\frac{{kr}^{2}}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}^{2}}{{Iz} \cdot V}} \right)\left( {\frac{1}{\sqrt{{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {\left( {1 - {Rfr}} \right)^{2} \cdot {Rlr\_ r}^{2} \cdot {Fa}^{2}}}} + \frac{1}{\sqrt{{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {\left( {1 - {Rfr}} \right)^{2} \cdot \left( {1 - {Rlr\_ r}} \right)^{2} \cdot {Fa}^{2}}}}} \right){{\beta \; f}}}} & (54)\end{matrix}$

Specifically, the values of the nonlinear term are calculatedsequentially based on the friction coefficient μ, the total drivingforce Fa, the vertical forces Ffl_z−Frr_z, and the average slidingangles βf and βr, while varying each of the distribution ratios Rfr,Rlr_f and Rlr_r in a stepwise manner from 0.00 through 1.00. Thereafter,the combination of the distribution ratios Rfr, Rlr_f and Rlr_r thatyields the smallest of the calculated nonlinear term values is selected,and those distribution ratios are set as the target values Rfr*, Rlr_f*and Rlr_r*. Note that in the above equations, the average front wheelsliding angle βf and the average rear wheel sliding angle βr may bereplaced with the respective wheel lateral forces Ffl_y−Frr_y. In thiscase, the nonlinear term of the divergence □S is expressed as follows:

$\begin{matrix}{{\left( {\frac{{kf}^{\;}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\;}}{{Iz} \cdot V}} \right)\left( {\frac{{Ffl\_ y}}{\sqrt{{\mu \; {{fl}^{2} \cdot {Ffl\_ z}^{2}}} - {{Rfr}^{2} \cdot {Rlr\_ f}^{2} \cdot {Fa}^{2}}}} + \frac{{Ffr\_ y}}{\sqrt{{\mu \; {{fr}^{2} \cdot {Ffr\_ z}^{2}}} - {{Rfr}^{2} \cdot \left( {1 - {Rlr\_ f}} \right)^{2} \cdot {Fa}^{2}}}}} \right)} + {\left( {\frac{kr}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}}{{Iz} \cdot V}} \right)\left( {\frac{{Frl\_ y}}{\sqrt{{\mu \; {{rl}^{2} \cdot {Frl\_ z}^{2}}} - {\left( {1 - {Rfr}} \right)^{2} \cdot {Rlr\_ r}^{2} \cdot {Fa}^{2}}}} + \frac{{Frr\_ y}}{\sqrt{{\mu \; {{rr}^{2} \cdot {Frr\_ z}^{2}}} - {\left( {1 - {Rfr}} \right)^{2} \cdot \left( {1 - {Rlr\_ r}} \right)^{2} \cdot {Fa}^{2}}}}} \right)}} & (55)\end{matrix}$

In the present embodiment, the driving force distribution ratios Rfr*,Rlr_f* and Rlr_r* are determined so as to minimize the divergence □S inthe vector field that represents the surface of state of the vehiclemotion. By distributing appropriately the driving force to the wheels,it is possible to achieve stable vehicle responses and thus improvesteering. Note that setting the front left/right distribution ratioRlr_f and the rear left/right distribution ratio Rlr_r to the constantvalue of 0.50 allows the distribution of the driving force equivalent tosimply distributing the driving force between the front and rear wheels.Methods for distributing the driving force to the left and right wheelsare described in, for example, Japanese Kokai Laid-open Publication2001-168385. The entire disclosure of Japanese Kokai Laid-openPublication 2001-168385 is incorporated herein by reference.

Ninth Embodiment

In the embodiments described above, the nonlinear terms were minimizedthrough adjusting the driving force distribution ratio for the wheels.However, because changes in the nonlinear terms are also caused by aload distribution ratio for the wheels, the nonlinear terms can beminimized through controlling the load distribution as well. Since thefundamental control concept is identical to that for controlling thedriving force distribution, only the differences between the twoapproaches are described in the present embodiment.

Here, the total load, which is the sum of the load on each of thewheels, is denoted by W, and the load distribution ratio between thefront and rear wheels is denoted by r′. Note that at this point, theaddition of the apostrophe does not indicate a derivative, as it does inthe previous embodiments. The average vertical force Ff_z for the frontwheels and the average vertical force Fr_z for the rear wheels are givenas follows:

$\begin{matrix}{{W = {2\left( {{Ff\_ z} + {Fr\_ z}} \right)}}{{Ff\_ z} = {r^{\prime} \cdot \frac{W}{2}}}{{Fr\_ z} = {\left( {1 - r^{\prime}} \right) \cdot \frac{W}{2}}}} & (56)\end{matrix}$

The load distribution ratio r′ that minimizes the nonlinear term in eachof the elements a11 through a22 can be determined uniquely based on Eqs.(40), (41), and (56), through replacing Eq. (43), described in thesecond embodiment, with Eq. (56). For example, the nonlinear term in theelement a11 is expressed as follows:

$\begin{matrix}{{\frac{{kf}^{\; 2}}{\sqrt{{\mu^{2} \cdot r^{\prime 2} \cdot \frac{W^{2}}{4}} - {Ff\_ x}^{2}}} \cdot {{\beta \; f}}} + {\frac{{kr}^{\; 2}}{\sqrt{{\mu^{2} \cdot \left( {1 - r^{\prime}} \right)^{2} \cdot \frac{W^{2}}{4}} - {Fr\_ x}^{2}}} \cdot {{\beta \; r}}}} & (57)\end{matrix}$

where the total load W can be defined uniquely as the sum of thevertical forces (detected values) Fz for the individual wheels. The loaddistribution ratio r′ that minimizes the nonlinear term can be obtaineduniquely based on the average front and rear wheel sliding angles βf andβr, the friction coefficient μ, the total load W, and the averagelongitudinal forces Ff_x and Fr_x for the front and rear wheels.

Moreover, this type of load distribution control can be applied not onlyto the method described in the second embodiment, but also to the otherembodiments as well. For example, in the fifth-seventh embodiments, theload distribution ratio r′ that minimizes the nonlinear terms in the sumof the elements a11 and a22 can be calculated as in Eq. (58), which isobtained by substituting Eq. (56) into the nonlinear term in Eq. (48):

$\begin{matrix}{{\left( {\frac{{kf}^{\; 2}}{M \cdot V} + \frac{{lf}^{\; 2} \cdot {kf}^{\; 2}}{{Iz} \cdot V}} \right){\left( \frac{1}{\sqrt{{\mu^{2} \cdot r^{2} \cdot \frac{W^{2}}{4}} - {Ff\_ x}^{2}}} \right) \cdot {{\beta \; f}}}} + {\left( {\frac{{kr}^{\; 2}}{M \cdot V} + \frac{{lr}^{2} \cdot {kr}^{2}}{{Iz} \cdot V}} \right){\left( \frac{1}{\sqrt{{\mu^{2} \cdot \left( {1 - r} \right)^{2} \cdot \frac{W^{2}}{4}} - {Fr\_ x}^{2}}} \right) \cdot {{\beta \; r}}}}} & (58)\end{matrix}$

As seen above, according to the present embodiment, the same effects asin the previous embodiments can be achieved, and the method of controlis versatile enough to be applied to a broad variety of vehicles. Notethat the load distribution to the individual wheels can be varieddynamically using electronically controlled suspension devices, forexample.

The various embodiments described above dealt with four-wheel drivevehicles that use an engine as the driving power source, but an electricmotor may be used as the driving power source instead. In such a case,the four wheels may all be driven by a single motor through adifferential device in the same way as for the engine, or each wheel maybe provided with a motor, or the front and rear wheels may be providedwith respective motors. Even in these situations, the appropriatedriving force distribution ratio r is obtained through controlling thedifferential of the differential device, or through controlling thepower of the individual motors directly, by focusing on the nonlinearterms in the elements in the system matrix. The same effects as in theprevious embodiments can be achieved in these situations as well.Moreover, for controlling during braking, power control of the engine,an antilock braking system, or the like, may be used depending on thedriving force distribution ratio r.

Further, in the various embodiments described above, the detecting unit81 was structured to detect the applied forces in three directions;however, the present invention is not limited thereto, but rather anydetection system may be used insofar as it is able to detect thecomponents of the applied forces in the required directions. Moreover,the directional components are not limited to three directions, butrather six-component force meters may be used to detect six componentsof a force, including the moments in three axes of rotation. Suchstructures pose, of course, no problem as long as they can detect, atleast, the required applied forces. Note that a method for detecting thesix components of the force that is applied to each of the wheels isdescribed in, for example, Japanese Kokai Laid-open Publication2002-039744 and Japanese Kokai Laid-open Publication 2002-022579. Theentire disclosures of Japanese Kokai Laid-open Publications 2002-039744and 2002-022579 are incorporated herein by reference.

A case wherein the detecting unit 81 is embedded in the axle 75 wasdescribed above, but the present invention is not limited thereto, andother variations can also be contemplated. From the perspective ofdetecting applied forces, the detecting unit 81 may be provided in, forexample, a member that holds the wheels 76, such as a hub or a hubcarrier, or the like. A method wherein the detecting unit is provided ina hub is described in Japanese Kokai Laid-open Publication 2003-104139.The entire disclosure of Japanese Kokai Laid-open Publication2003-104139 is incorporated herein by reference.

In the embodiments presented, the longitudinal force Fx, lateral forceFy, and vertical force Fz were detected by sensors that detect directlythe applied forces in three directions; however, the present inventionis not limited thereto. For example, the lateral force Fy may bedetermined through estimating the cornering force (that is detectable),and the vertical force Fz may be determined through estimating thevertical load (that is detectable). In these estimating methods, wheelvelocity sensors that detect the velocities of individual wheels,lateral acceleration sensors and longitudinal acceleration sensors thatare provided at the center of gravity of the vehicle, and yaw ratesensors may be used.

The method for estimating the cornering force is explained below. As forthe detection values obtained from the various sensors, the velocitiesof the individual wheels are denoted by Vfl_s, Vfr_s, Vrl_s, and Vrr_s,the yaw rate is denoted by y, the lateral acceleration is denoted byy″s, and the longitudinal acceleration is denoted by x″s. Moreover, theheight of the center of gravity is denoted by h, the tread width isdenoted by d, and the acceleration due to gravity is denoted by g.

These detected values are subjected to a digital filtering process forthe purpose of eliminating noise due to road surface cant and vehiclebody roll, in addition to low-frequency noise and high-frequency noise.The values detected by the wheel velocity sensors (wheel velocities),after the filtering processes, are denoted by Vfl_f, Vfr_f, Vrl_f, andVrr_f, the vehicle velocity estimated based on these values (forexample, the average value of the individual wheel velocities) isdenoted by V̂, and the vehicle acceleration obtained through taking thederivative of the vehicle speed V̂ is denoted by x″̂. Moreover, the outputvalue from the yaw rate sensor (the yaw rate), after the filteringprocess, is denoted by γf, and the yaw angular acceleration obtainedthrough taking the derivative of the yaw rate γf is denoted by γ′̂. Thevalue outputted from the lateral acceleration sensor (the lateralacceleration), after the filtering process, is denoted by y″̂.

In the following, the left and right front wheel cornering forces aredenoted by Ffl̂ and Ffr̂, and the left and right rear wheel corneringforces are denoted by Frl̂ and Frr̂. These values can be estimated usingthe equations of motion and the relationships below:

$\begin{matrix}{{{Ffl}^{\bigwedge} = {{Ffr}^{\bigwedge} = {\frac{1}{2} \cdot \frac{{{lr} \cdot M \cdot y^{''\bigwedge}} + {{Iz} \cdot \gamma^{\prime\bigwedge}}}{{lf} + {lr}}}}}{{Frl}^{\bigwedge} = {{Frr}^{\bigwedge} = {\frac{1}{2} \cdot \frac{{{lf} \cdot M \cdot y^{''\bigwedge}} - {{Iz} \cdot \gamma^{\prime\bigwedge}}}{{lf} + {lr}}}}}} & (59)\end{matrix}$

Consequently, the estimated value Ff̂ for the average cornering force ofthe front wheels and the estimated value Fr̂ for the average corneringforce of the rear wheels can be calculated uniquely as follows:

$\begin{matrix}{{{Ff}^{\;\bigwedge} = {\frac{{Ffl}^{\bigwedge} + {Ffr}^{\bigwedge}}{2} = {\frac{1}{2} \cdot \frac{{{lr} \cdot M \cdot y^{''\bigwedge}} + {{Iz} \cdot \gamma^{\prime\bigwedge}}}{{lf} + {lr}}}}}{{Fr}^{\bigwedge} = {\frac{{Frl}^{\bigwedge} + {Frr}^{\bigwedge}}{2} = {\frac{1}{2} \cdot \frac{{{lf} \cdot M \cdot y^{''\bigwedge}} - {{Iz} \cdot \gamma^{\prime\bigwedge}}}{{lf} + {lr}}}}}} & (60)\end{matrix}$

If the cornering force acting on the vehicle body is denoted by Fc, therelationship between the cornering force Fc and the lateral force Fyacting on the wheels 76 satisfy the following relationship:

Fy=Fc·cos δf  (61)

Next, the method of estimating the vertical load is explained below. Ifthe estimated values for the left and right front wheel vertical loadsare denoted by Wfl̂ and Wfr̂, and the estimated values for the verticalloads on the left and right rear wheels are denoted by Wrl̂ and Wrr̂,these estimated values can be obtained as follows, ignoring theaccelerating motion in the vertical direction and ignoring theaccelerating motions around the roll and pitch axes of rotation:

$\begin{matrix}{{{Wfl}^{\bigwedge} = {{\frac{1}{2} \cdot \frac{lr}{{lf} + {lr}} \cdot M \cdot g} - {\Delta \; {Wlong}} - {\Delta \; {Wlat}}}}{{Wfr}^{\bigwedge} = {{\frac{1}{2} \cdot \frac{lr}{{lf} + {lr}} \cdot M \cdot g} - {\Delta \; {Wlong}} + {\Delta \; {Wlat}}}}{{Wrl}^{\bigwedge} = {{\frac{1}{2} \cdot \frac{lf}{{lf} + {lr}} \cdot M \cdot g} + {\Delta \; {Wlong}} - {\Delta \; {Wlat}}}}{{Wrr}^{\bigwedge} = {{\frac{1}{2} \cdot \frac{lf}{{lf} + {lr}} \cdot M \cdot g} + {\Delta \; {Wlong}} + {\Delta \; {Wlat}}}}} & (62)\end{matrix}$

Consequently, the estimated value Ff̂ of the average cornering force forthe front wheels and the estimated value Fr̂ of the average corneringforce for the rear wheels can be obtained as follows:

$\begin{matrix}{{{Wf}^{\;\bigwedge} = {\frac{{Wfl}^{\bigwedge} + {Wfr}^{\bigwedge}}{2} = {{\frac{1}{2} \cdot \frac{lr}{{lf} + {lr}} \cdot M \cdot g} - {\Delta \; {Wlong}}}}}{{Wr}^{\bigwedge} = {\frac{{Wrl}^{\bigwedge} + {Wrr}^{\bigwedge}}{2} = {{\frac{1}{2} \cdot \frac{lf}{{lf} + {lr}} \cdot M \cdot g} + {\Delta \; {Wlong}}}}}} & (63)\end{matrix}$

where ΔWlong is the amount of shift of the load due to longitudinalacceleration, and ΔWlat is the amount of shift of the load due tolateral acceleration. These individual values can be obtained asfollows:

$\begin{matrix}{{{\Delta \; {Wlong}} = {\frac{1}{2} \cdot \frac{h}{{lf} + {lr}} \cdot M \cdot {ax}}}{{\Delta \; {Wlat}} = {\frac{1}{2} \cdot \frac{h}{d} \cdot M \cdot {ay}}}} & (64)\end{matrix}$

where ax is the longitudinal acceleration, which is the output value x″sfrom the longitudinal acceleration sensor or the vehicle bodyacceleration x″̂ calculated based on the wheel velocity, and ay is thelateral acceleration, which is the output value y″̂ from the lateralacceleration sensor. Although in the calculations described above, theacceleration motions in the vertical direction on the springs and therotational motion around the roll and pitch axes of rotation areignored, the cornering force and the vertical load may be estimatedtaking these factors into account as well.

It is to be understood that the above-described embodiments areillustrative of only a few of the many possible specific embodimentswhich can represent applications of the principles of the invention.Numerous and varied other arrangements can be readily devised by thoseskilled in the art without departing from the spirit and scope of theinvention.

1. A vehicle motion control device for a vehicle, the vehicle having aplurality of wheels and a driving device for driving the wheels based ona driving force/load distribution ratio, comprising: a calculating unitfor obtaining, based on equations of state that describe a state ofmotion of the vehicle, a divergence value, which is a characteristicvalue that represents a tendency of vectors in a vector field, thevector field describing a state surface with axes representing statevariables for the state of motion of the vehicle; a setting unit forsetting a target value of the driving force/load distribution ratio forthe individual wheels, such that the divergence value becomes less thana current value of the divergence value or the divergence value becomesless than or equal to zero; and a driving device control unit forcontrolling the driving device based on the target driving force/loaddistribution ratio.
 2. A vehicle motion control device for a vehicle,the vehicle having a plurality of wheels and a driving device fordriving the wheels based on a driving force/load distribution ratio,comprising: a calculating unit for obtaining, based on equations ofstate that describe a state of motion of the vehicle, a damping value,which is a characteristic value that represents a convergence of thevehicle as an oscillator system; a setting unit for setting a targetvalue of the driving force/load distribution ratio for the individualwheels, such that the damping value becomes larger than a current valueof the damping value; and a driving device control unit for controllingthe driving device based on the target value of the driving force/loaddistribution ratio.
 3. The vehicle motion control device according toclaim 1, further comprising: a detector unit for detecting a verticalforce that acts on each of the wheels; and an estimating unit forestimating a sum of driving forces transmitted to the individual wheelsto obtain an estimated total driving force, and estimating a frictioncoefficient between the wheels and a road surface to obtain an estimatedfriction coefficient; wherein the calculating unit obtains nonlinearterms in a polynomial that is a sum of diagonal elements of a systemmatrix for equations of state, the nonlinear terms comprising a slidingangle of the front wheels and a sliding angle of the rear wheels asvariables, for each of the driving force distribution ratios, based on agroup of parameters including the vertical force for each of the wheels,the estimated friction coefficient, and the estimated total drivingforce; and wherein the setting unit sets a target value of the drivingforce distribution ratio based on each of the nonlinear terms obtainedin the calculating unit.
 4. The vehicle motion control device accordingto claim 2, further comprising: a detector unit for detecting a verticalforce that acts on each of the wheels; and an estimating unit forestimating a sum of driving forces transmitted to the individual wheelsto obtain an estimated total driving force, and estimating a frictioncoefficient between the wheels and a road surface to obtain an estimatedfriction coefficient; wherein the calculating unit obtains nonlinearterms in a polynomial that is a sum of diagonal elements of a systemmatrix for equations of state, the nonlinear terms comprising a slidingangle of the front wheels and a sliding angle of the rear wheels asvariables, for each of the driving force distribution ratios, based on agroup of parameters including the vertical force for each of the wheels,the estimated friction coefficient, and the estimated total drivingforce; and wherein the setting unit sets a target value of the drivingforce distribution ratio based on each of the nonlinear terms obtainedin the calculating unit.
 5. The vehicle motion control device accordingto claim 1, further comprising; a detector unit for detecting a verticalforce and a longitudinal force that act on each of the wheels; and anestimating unit for estimating a friction coefficient between the wheelsand a road surface to obtain an estimated friction coefficient; whereinthe calculating unit obtains nonlinear terms in a polynomial that is asum of diagonal elements of a system matrix for equations of state, thenonlinear terms comprising a sliding angle of the front wheels and asliding angle of the rear wheels as variables, for each of the loaddistribution ratios, based on a group of parameters including thevertical force and the longitudinal force for each of the wheels and theestimated friction coefficient; and wherein the setting unit sets atarget value of the load distribution ratio based on each of thenonlinear terms.
 6. The vehicle motion control device according to claim2, further comprising; a detector unit for detecting a vertical forceand a longitudinal force that act on each of the wheels; and anestimating unit for estimating a friction coefficient between the wheelsand a road surface to obtain an estimated friction coefficient; whereinthe calculating unit obtains nonlinear terms in a polynomial that is asum of diagonal elements of a system matrix for equations of state, thenonlinear terms comprising a sliding angle of the front wheels and asliding angle of the rear wheels as variables, for each of the loaddistribution ratios, based on a group of parameters including thevertical force and the longitudinal force for each of the wheels and theestimated friction coefficient; and wherein the setting unit sets atarget value of the load distribution ratio based on each of thenonlinear terms.
 7. A vehicle motion control method for controllingmotion of a vehicle, the vehicle having a plurality of wheels and adriving device for driving the wheels based on a driving force/loaddistribution ratio, comprising: a calculating step for obtaining, basedon equations of state that describe a state of motion of the vehicle, adivergence value, which is a characteristic value that represents atendency of vectors in a vector field, the vector field describing astate surface with axes representing state variables for the state ofmotion of the vehicle; a setting step for setting a target value of thedriving force/load distribution ratio for the individual wheels, suchthat the divergence value becomes less than a current value of thedivergence value or the divergence value becomes less than or equal tozero; and a driving device control step for controlling the drivingdevice based on the target driving force/load distribution ratio.
 8. Avehicle motion control method for controlling motion of a vehicle, thevehicle having a plurality of wheels and a driving device for drivingthe wheels based on a driving force/load distribution ratio, comprising:a calculating step for obtaining, based on equations of state thatdescribe a state of motion of the vehicle, a damping value, which is acharacteristic value that represents a convergence of the vehicle as anoscillator system; a setting step for setting a target value of thedriving force/load distribution ratio for the individual wheels, suchthat the damping value becomes larger than a current value of thedamping value; and a driving device control step for controlling thedriving device based on the target value of the driving force/loaddistribution ratio.